Spherical CR geometry and Dehn surgery /:
This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds whic...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton :
Princeton University Press,
2007.
|
| Schriftenreihe: | Annals of mathematics studies ;
no. 165. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds which bound complex hyperbolic orbifolds--the only known examples of closed manifolds that simultaneously have these two kinds of geometric structures. The second is a complete understanding of the structure of complex hyperbolic reflection triangle groups in cases where the angle is small. In an accessib. |
| Beschreibung: | 1 online resource (xii, 186 pages :) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliographie: | Includes bibliographical references (pages 181-184) and index. |
| ISBN: | 9780691128108 0691128103 9781400837199 1400837197 069112809X 9780691128092 |
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| 100 | 1 | |a Schwartz, Richard Evan. |0 http://id.loc.gov/authorities/names/nr91012881 | |
| 245 | 1 | 0 | |a Spherical CR geometry and Dehn surgery / |c Richard Evan Schwartz. |
| 260 | |a Princeton : |b Princeton University Press, |c 2007. | ||
| 300 | |a 1 online resource (xii, 186 pages :) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a Annals of mathematics studies ; |v no. 165 | |
| 504 | |a Includes bibliographical references (pages 181-184) and index. | ||
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2010. |5 MiAaHDL | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2010 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. BASIC MATERIAL; Chapter 1. Introduction; 1.1 Dehn Filling and Thurston's Theorem; 1.2 Definition of a Horotube Group; 1.3 The Horotube Surgery Theorem; 1.4 Reflection Triangle Groups; 1.5 Spherical CR Structures; 1.6 The Goldman-Parker Conjecture; 1.7 Organizational Notes; Chapter 2. Rank-One Geometry; 2.1 Real Hyperbolic Geometry; 2.2 Complex Hyperbolic Geometry; 2.3 The Siegel Domain and Heisenberg Space; 2.4 The Heisenberg Contact Form; 2.5 Some Invariant Functions; 2.6 Some Geometric Objects. | |
| 505 | 8 | |a Chapter 3. Topological Generalities3.1 The Hausdorff Topology; 3.2 Singular Models and Spines; 3.3 A Transversality Result; 3.4 Discrete Groups; 3.5 Geometric Structures; 3.6 Orbifold Fundamental Groups; 3.7 Orbifolds with Boundary; Chapter 4. Reflection Triangle Groups; 4.1 The Real Hyperbolic Case; 4.2 The Action on the Unit Tangent Bundle; 4.3 Fuchsian Triangle Groups; 4.4 Complex Hyperbolic Triangles; 4.5 The Representation Space; 4.6 The Ideal Case; Chapter 5. Heuristic Discussion of Geometric Filling; 5.1 A Dictionary; 5.2 The Tree Example; 5.3 Hyperbolic Case: Before Filling. | |
| 505 | 8 | |a 5.4 Hyperbolic Case: After Filling5.5 Spherical CR Case: Before Filling; 5.6 Spherical CR Case: After Filling; 5.7 The Tree Example Revisited; PART 2. PROOF OF THE HST; Chapter 6. Extending Horotube Functions; 6.1 Statement of Results; 6.2 Proof of the Extension Lemma; 6.3 Proof of the Auxiliary Lemma; Chapter 7. Transplanting Horotube Functions; 7.1 Statement of Results; 7.2 A Toy Case; 7.3 Proof of the Transplant Lemma; Chapter 8. The Local Surgery Formula; 8.1 Statement of Results; 8.2 The Canonical Marking; 8.3 The Homeomorphism; 8.4 The Surgery Formula; Chapter 9. Horotube Assignments. | |
| 505 | 8 | |a 9.1 Basic Definitions9.2 The Main Result; 9.3 Corollaries; Chapter 10. Constructing the Boundary Complex; 10.1 Statement of Results; 10.2 Proof of the Structure Lemma; 10.3 Proof of the Horotube Assignment Lemma; Chapter 11. Extending to the Inside; 11.1 Statement of Results; 11.2 Proof of the Transversality Lemma; 11.3 Proof of the Local Structure Lemma; 11.4 Proof of the Compatibility Lemma; 11.5 Proof of the Finiteness Lemma; Chapter 12. Machinery for Proving Discreteness; 12.1 Chapter Overview; 12.2 Simple Complexes; 12.3 Chunks; 12.4 Geometric Equivalence Relations. | |
| 505 | 8 | |a 12.5 Alignment by a Simple ComplexChapter 13. Proof of the HST; 13.1 The Unperturbed Case; 13.2 The Perturbed Case; 13.3 Defining the Chunks; 13.4 The Discreteness Proof; 13.5 The Surgery Formula; 13.6 Horotube Group Structure; 13.7 Proof of Theorem 1.11; 13.8 Dealing with Elliptics; PART 3. THE APPLICATIONS; Chapter 14. The Convergence Lemmas; 14.1 Statement of Results; 14.2 Preliminary Lemmas; 14.3 Proof of the Convergence Lemma I; 14.4 Proof of the Convergence Lemma II; 14.5 Proof of the Convergence Lemma III; Chapter 15. Cusp Flexibility; 15.1 Statement of Results. | |
| 520 | |a This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds which bound complex hyperbolic orbifolds--the only known examples of closed manifolds that simultaneously have these two kinds of geometric structures. The second is a complete understanding of the structure of complex hyperbolic reflection triangle groups in cases where the angle is small. In an accessib. | ||
| 546 | |a English. | ||
| 650 | 0 | |a CR submanifolds. |0 http://id.loc.gov/authorities/subjects/sh85129485 | |
| 650 | 0 | |a Dehn surgery (Topology) |0 http://id.loc.gov/authorities/subjects/sh2006006222 | |
| 650 | 0 | |a Three-manifolds (Topology) |0 http://id.loc.gov/authorities/subjects/sh85135028 | |
| 650 | 6 | |a CR-sous-variétés. | |
| 650 | 6 | |a Chirurgie de Dehn (Topologie) | |
| 650 | 6 | |a Variétés topologiques à 3 dimensions. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Differential. |2 bisacsh | |
| 650 | 7 | |a CR submanifolds |2 fast | |
| 650 | 7 | |a Dehn surgery (Topology) |2 fast | |
| 650 | 7 | |a Three-manifolds (Topology) |2 fast | |
| 758 | |i has work: |a Spherical CR geometry and Dehn surgery (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGJqVQ8Q73xyq7YGtXbG9C |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 773 | 0 | |t Academic Search Complete |d EBSCO | |
| 776 | 0 | 8 | |i Print version: |a Schwartz, Richard Evan. |t Spherical CR geometry and Dehn surgery. |d Princeton : Princeton University Press, 2007 |w (DLC) 2006050589 |w (OCoLC)71237491 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 165. |0 http://id.loc.gov/authorities/names/n42002129 | |
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| author | Schwartz, Richard Evan |
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| contents | Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. BASIC MATERIAL; Chapter 1. Introduction; 1.1 Dehn Filling and Thurston's Theorem; 1.2 Definition of a Horotube Group; 1.3 The Horotube Surgery Theorem; 1.4 Reflection Triangle Groups; 1.5 Spherical CR Structures; 1.6 The Goldman-Parker Conjecture; 1.7 Organizational Notes; Chapter 2. Rank-One Geometry; 2.1 Real Hyperbolic Geometry; 2.2 Complex Hyperbolic Geometry; 2.3 The Siegel Domain and Heisenberg Space; 2.4 The Heisenberg Contact Form; 2.5 Some Invariant Functions; 2.6 Some Geometric Objects. Chapter 3. Topological Generalities3.1 The Hausdorff Topology; 3.2 Singular Models and Spines; 3.3 A Transversality Result; 3.4 Discrete Groups; 3.5 Geometric Structures; 3.6 Orbifold Fundamental Groups; 3.7 Orbifolds with Boundary; Chapter 4. Reflection Triangle Groups; 4.1 The Real Hyperbolic Case; 4.2 The Action on the Unit Tangent Bundle; 4.3 Fuchsian Triangle Groups; 4.4 Complex Hyperbolic Triangles; 4.5 The Representation Space; 4.6 The Ideal Case; Chapter 5. Heuristic Discussion of Geometric Filling; 5.1 A Dictionary; 5.2 The Tree Example; 5.3 Hyperbolic Case: Before Filling. 5.4 Hyperbolic Case: After Filling5.5 Spherical CR Case: Before Filling; 5.6 Spherical CR Case: After Filling; 5.7 The Tree Example Revisited; PART 2. PROOF OF THE HST; Chapter 6. Extending Horotube Functions; 6.1 Statement of Results; 6.2 Proof of the Extension Lemma; 6.3 Proof of the Auxiliary Lemma; Chapter 7. Transplanting Horotube Functions; 7.1 Statement of Results; 7.2 A Toy Case; 7.3 Proof of the Transplant Lemma; Chapter 8. The Local Surgery Formula; 8.1 Statement of Results; 8.2 The Canonical Marking; 8.3 The Homeomorphism; 8.4 The Surgery Formula; Chapter 9. Horotube Assignments. 9.1 Basic Definitions9.2 The Main Result; 9.3 Corollaries; Chapter 10. Constructing the Boundary Complex; 10.1 Statement of Results; 10.2 Proof of the Structure Lemma; 10.3 Proof of the Horotube Assignment Lemma; Chapter 11. Extending to the Inside; 11.1 Statement of Results; 11.2 Proof of the Transversality Lemma; 11.3 Proof of the Local Structure Lemma; 11.4 Proof of the Compatibility Lemma; 11.5 Proof of the Finiteness Lemma; Chapter 12. Machinery for Proving Discreteness; 12.1 Chapter Overview; 12.2 Simple Complexes; 12.3 Chunks; 12.4 Geometric Equivalence Relations. 12.5 Alignment by a Simple ComplexChapter 13. Proof of the HST; 13.1 The Unperturbed Case; 13.2 The Perturbed Case; 13.3 Defining the Chunks; 13.4 The Discreteness Proof; 13.5 The Surgery Formula; 13.6 Horotube Group Structure; 13.7 Proof of Theorem 1.11; 13.8 Dealing with Elliptics; PART 3. THE APPLICATIONS; Chapter 14. The Convergence Lemmas; 14.1 Statement of Results; 14.2 Preliminary Lemmas; 14.3 Proof of the Convergence Lemma I; 14.4 Proof of the Convergence Lemma II; 14.5 Proof of the Convergence Lemma III; Chapter 15. Cusp Flexibility; 15.1 Statement of Results. |
| ctrlnum | (OCoLC)680126444 |
| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.</subfield><subfield code="u">http://purl.oclc.org/DLF/benchrepro0212</subfield><subfield code="5">MiAaHDL</subfield></datafield><datafield tag="583" ind1="1" ind2=" "><subfield code="a">digitized</subfield><subfield code="c">2010</subfield><subfield code="h">HathiTrust Digital Library</subfield><subfield code="l">committed to preserve</subfield><subfield code="2">pda</subfield><subfield code="5">MiAaHDL</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. BASIC MATERIAL; Chapter 1. Introduction; 1.1 Dehn Filling and Thurston's Theorem; 1.2 Definition of a Horotube Group; 1.3 The Horotube Surgery Theorem; 1.4 Reflection Triangle Groups; 1.5 Spherical CR Structures; 1.6 The Goldman-Parker Conjecture; 1.7 Organizational Notes; Chapter 2. Rank-One Geometry; 2.1 Real Hyperbolic Geometry; 2.2 Complex Hyperbolic Geometry; 2.3 The Siegel Domain and Heisenberg Space; 2.4 The Heisenberg Contact Form; 2.5 Some Invariant Functions; 2.6 Some Geometric Objects.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Chapter 3. Topological Generalities3.1 The Hausdorff Topology; 3.2 Singular Models and Spines; 3.3 A Transversality Result; 3.4 Discrete Groups; 3.5 Geometric Structures; 3.6 Orbifold Fundamental Groups; 3.7 Orbifolds with Boundary; Chapter 4. Reflection Triangle Groups; 4.1 The Real Hyperbolic Case; 4.2 The Action on the Unit Tangent Bundle; 4.3 Fuchsian Triangle Groups; 4.4 Complex Hyperbolic Triangles; 4.5 The Representation Space; 4.6 The Ideal Case; Chapter 5. Heuristic Discussion of Geometric Filling; 5.1 A Dictionary; 5.2 The Tree Example; 5.3 Hyperbolic Case: Before Filling.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">5.4 Hyperbolic Case: After Filling5.5 Spherical CR Case: Before Filling; 5.6 Spherical CR Case: After Filling; 5.7 The Tree Example Revisited; PART 2. PROOF OF THE HST; Chapter 6. Extending Horotube Functions; 6.1 Statement of Results; 6.2 Proof of the Extension Lemma; 6.3 Proof of the Auxiliary Lemma; Chapter 7. Transplanting Horotube Functions; 7.1 Statement of Results; 7.2 A Toy Case; 7.3 Proof of the Transplant Lemma; Chapter 8. The Local Surgery Formula; 8.1 Statement of Results; 8.2 The Canonical Marking; 8.3 The Homeomorphism; 8.4 The Surgery Formula; Chapter 9. Horotube Assignments.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">9.1 Basic Definitions9.2 The Main Result; 9.3 Corollaries; Chapter 10. Constructing the Boundary Complex; 10.1 Statement of Results; 10.2 Proof of the Structure Lemma; 10.3 Proof of the Horotube Assignment Lemma; Chapter 11. Extending to the Inside; 11.1 Statement of Results; 11.2 Proof of the Transversality Lemma; 11.3 Proof of the Local Structure Lemma; 11.4 Proof of the Compatibility Lemma; 11.5 Proof of the Finiteness Lemma; Chapter 12. Machinery for Proving Discreteness; 12.1 Chapter Overview; 12.2 Simple Complexes; 12.3 Chunks; 12.4 Geometric Equivalence Relations.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">12.5 Alignment by a Simple ComplexChapter 13. Proof of the HST; 13.1 The Unperturbed Case; 13.2 The Perturbed Case; 13.3 Defining the Chunks; 13.4 The Discreteness Proof; 13.5 The Surgery Formula; 13.6 Horotube Group Structure; 13.7 Proof of Theorem 1.11; 13.8 Dealing with Elliptics; PART 3. THE APPLICATIONS; Chapter 14. The Convergence Lemmas; 14.1 Statement of Results; 14.2 Preliminary Lemmas; 14.3 Proof of the Convergence Lemma I; 14.4 Proof of the Convergence Lemma II; 14.5 Proof of the Convergence Lemma III; Chapter 15. Cusp Flexibility; 15.1 Statement of Results.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. 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| id | ZDB-4-EBA-ocn680126444 |
| illustrated | Illustrated |
| indexdate | 2025-03-18T14:15:23Z |
| institution | BVB |
| isbn | 9780691128108 0691128103 9781400837199 1400837197 069112809X 9780691128092 |
| language | English |
| lccn | 2006050589 |
| oclc_num | 680126444 |
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| series | Annals of mathematics studies ; |
| series2 | Annals of mathematics studies ; |
| spelling | Schwartz, Richard Evan. http://id.loc.gov/authorities/names/nr91012881 Spherical CR geometry and Dehn surgery / Richard Evan Schwartz. Princeton : Princeton University Press, 2007. 1 online resource (xii, 186 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier Annals of mathematics studies ; no. 165 Includes bibliographical references (pages 181-184) and index. Use copy Restrictions unspecified star MiAaHDL Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2010. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL Print version record. Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. BASIC MATERIAL; Chapter 1. Introduction; 1.1 Dehn Filling and Thurston's Theorem; 1.2 Definition of a Horotube Group; 1.3 The Horotube Surgery Theorem; 1.4 Reflection Triangle Groups; 1.5 Spherical CR Structures; 1.6 The Goldman-Parker Conjecture; 1.7 Organizational Notes; Chapter 2. Rank-One Geometry; 2.1 Real Hyperbolic Geometry; 2.2 Complex Hyperbolic Geometry; 2.3 The Siegel Domain and Heisenberg Space; 2.4 The Heisenberg Contact Form; 2.5 Some Invariant Functions; 2.6 Some Geometric Objects. Chapter 3. Topological Generalities3.1 The Hausdorff Topology; 3.2 Singular Models and Spines; 3.3 A Transversality Result; 3.4 Discrete Groups; 3.5 Geometric Structures; 3.6 Orbifold Fundamental Groups; 3.7 Orbifolds with Boundary; Chapter 4. Reflection Triangle Groups; 4.1 The Real Hyperbolic Case; 4.2 The Action on the Unit Tangent Bundle; 4.3 Fuchsian Triangle Groups; 4.4 Complex Hyperbolic Triangles; 4.5 The Representation Space; 4.6 The Ideal Case; Chapter 5. Heuristic Discussion of Geometric Filling; 5.1 A Dictionary; 5.2 The Tree Example; 5.3 Hyperbolic Case: Before Filling. 5.4 Hyperbolic Case: After Filling5.5 Spherical CR Case: Before Filling; 5.6 Spherical CR Case: After Filling; 5.7 The Tree Example Revisited; PART 2. PROOF OF THE HST; Chapter 6. Extending Horotube Functions; 6.1 Statement of Results; 6.2 Proof of the Extension Lemma; 6.3 Proof of the Auxiliary Lemma; Chapter 7. Transplanting Horotube Functions; 7.1 Statement of Results; 7.2 A Toy Case; 7.3 Proof of the Transplant Lemma; Chapter 8. The Local Surgery Formula; 8.1 Statement of Results; 8.2 The Canonical Marking; 8.3 The Homeomorphism; 8.4 The Surgery Formula; Chapter 9. Horotube Assignments. 9.1 Basic Definitions9.2 The Main Result; 9.3 Corollaries; Chapter 10. Constructing the Boundary Complex; 10.1 Statement of Results; 10.2 Proof of the Structure Lemma; 10.3 Proof of the Horotube Assignment Lemma; Chapter 11. Extending to the Inside; 11.1 Statement of Results; 11.2 Proof of the Transversality Lemma; 11.3 Proof of the Local Structure Lemma; 11.4 Proof of the Compatibility Lemma; 11.5 Proof of the Finiteness Lemma; Chapter 12. Machinery for Proving Discreteness; 12.1 Chapter Overview; 12.2 Simple Complexes; 12.3 Chunks; 12.4 Geometric Equivalence Relations. 12.5 Alignment by a Simple ComplexChapter 13. Proof of the HST; 13.1 The Unperturbed Case; 13.2 The Perturbed Case; 13.3 Defining the Chunks; 13.4 The Discreteness Proof; 13.5 The Surgery Formula; 13.6 Horotube Group Structure; 13.7 Proof of Theorem 1.11; 13.8 Dealing with Elliptics; PART 3. THE APPLICATIONS; Chapter 14. The Convergence Lemmas; 14.1 Statement of Results; 14.2 Preliminary Lemmas; 14.3 Proof of the Convergence Lemma I; 14.4 Proof of the Convergence Lemma II; 14.5 Proof of the Convergence Lemma III; Chapter 15. Cusp Flexibility; 15.1 Statement of Results. This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds which bound complex hyperbolic orbifolds--the only known examples of closed manifolds that simultaneously have these two kinds of geometric structures. The second is a complete understanding of the structure of complex hyperbolic reflection triangle groups in cases where the angle is small. In an accessib. English. CR submanifolds. http://id.loc.gov/authorities/subjects/sh85129485 Dehn surgery (Topology) http://id.loc.gov/authorities/subjects/sh2006006222 Three-manifolds (Topology) http://id.loc.gov/authorities/subjects/sh85135028 CR-sous-variétés. Chirurgie de Dehn (Topologie) Variétés topologiques à 3 dimensions. MATHEMATICS Geometry Differential. bisacsh CR submanifolds fast Dehn surgery (Topology) fast Three-manifolds (Topology) fast has work: Spherical CR geometry and Dehn surgery (Text) https://id.oclc.org/worldcat/entity/E39PCGJqVQ8Q73xyq7YGtXbG9C https://id.oclc.org/worldcat/ontology/hasWork Academic Search Complete EBSCO Print version: Schwartz, Richard Evan. Spherical CR geometry and Dehn surgery. Princeton : Princeton University Press, 2007 (DLC) 2006050589 (OCoLC)71237491 Annals of mathematics studies ; no. 165. http://id.loc.gov/authorities/names/n42002129 |
| spellingShingle | Schwartz, Richard Evan Spherical CR geometry and Dehn surgery / Annals of mathematics studies ; Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. BASIC MATERIAL; Chapter 1. Introduction; 1.1 Dehn Filling and Thurston's Theorem; 1.2 Definition of a Horotube Group; 1.3 The Horotube Surgery Theorem; 1.4 Reflection Triangle Groups; 1.5 Spherical CR Structures; 1.6 The Goldman-Parker Conjecture; 1.7 Organizational Notes; Chapter 2. Rank-One Geometry; 2.1 Real Hyperbolic Geometry; 2.2 Complex Hyperbolic Geometry; 2.3 The Siegel Domain and Heisenberg Space; 2.4 The Heisenberg Contact Form; 2.5 Some Invariant Functions; 2.6 Some Geometric Objects. Chapter 3. Topological Generalities3.1 The Hausdorff Topology; 3.2 Singular Models and Spines; 3.3 A Transversality Result; 3.4 Discrete Groups; 3.5 Geometric Structures; 3.6 Orbifold Fundamental Groups; 3.7 Orbifolds with Boundary; Chapter 4. Reflection Triangle Groups; 4.1 The Real Hyperbolic Case; 4.2 The Action on the Unit Tangent Bundle; 4.3 Fuchsian Triangle Groups; 4.4 Complex Hyperbolic Triangles; 4.5 The Representation Space; 4.6 The Ideal Case; Chapter 5. Heuristic Discussion of Geometric Filling; 5.1 A Dictionary; 5.2 The Tree Example; 5.3 Hyperbolic Case: Before Filling. 5.4 Hyperbolic Case: After Filling5.5 Spherical CR Case: Before Filling; 5.6 Spherical CR Case: After Filling; 5.7 The Tree Example Revisited; PART 2. PROOF OF THE HST; Chapter 6. Extending Horotube Functions; 6.1 Statement of Results; 6.2 Proof of the Extension Lemma; 6.3 Proof of the Auxiliary Lemma; Chapter 7. Transplanting Horotube Functions; 7.1 Statement of Results; 7.2 A Toy Case; 7.3 Proof of the Transplant Lemma; Chapter 8. The Local Surgery Formula; 8.1 Statement of Results; 8.2 The Canonical Marking; 8.3 The Homeomorphism; 8.4 The Surgery Formula; Chapter 9. Horotube Assignments. 9.1 Basic Definitions9.2 The Main Result; 9.3 Corollaries; Chapter 10. Constructing the Boundary Complex; 10.1 Statement of Results; 10.2 Proof of the Structure Lemma; 10.3 Proof of the Horotube Assignment Lemma; Chapter 11. Extending to the Inside; 11.1 Statement of Results; 11.2 Proof of the Transversality Lemma; 11.3 Proof of the Local Structure Lemma; 11.4 Proof of the Compatibility Lemma; 11.5 Proof of the Finiteness Lemma; Chapter 12. Machinery for Proving Discreteness; 12.1 Chapter Overview; 12.2 Simple Complexes; 12.3 Chunks; 12.4 Geometric Equivalence Relations. 12.5 Alignment by a Simple ComplexChapter 13. Proof of the HST; 13.1 The Unperturbed Case; 13.2 The Perturbed Case; 13.3 Defining the Chunks; 13.4 The Discreteness Proof; 13.5 The Surgery Formula; 13.6 Horotube Group Structure; 13.7 Proof of Theorem 1.11; 13.8 Dealing with Elliptics; PART 3. THE APPLICATIONS; Chapter 14. The Convergence Lemmas; 14.1 Statement of Results; 14.2 Preliminary Lemmas; 14.3 Proof of the Convergence Lemma I; 14.4 Proof of the Convergence Lemma II; 14.5 Proof of the Convergence Lemma III; Chapter 15. Cusp Flexibility; 15.1 Statement of Results. CR submanifolds. http://id.loc.gov/authorities/subjects/sh85129485 Dehn surgery (Topology) http://id.loc.gov/authorities/subjects/sh2006006222 Three-manifolds (Topology) http://id.loc.gov/authorities/subjects/sh85135028 CR-sous-variétés. Chirurgie de Dehn (Topologie) Variétés topologiques à 3 dimensions. MATHEMATICS Geometry Differential. bisacsh CR submanifolds fast Dehn surgery (Topology) fast Three-manifolds (Topology) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85129485 http://id.loc.gov/authorities/subjects/sh2006006222 http://id.loc.gov/authorities/subjects/sh85135028 |
| title | Spherical CR geometry and Dehn surgery / |
| title_auth | Spherical CR geometry and Dehn surgery / |
| title_exact_search | Spherical CR geometry and Dehn surgery / |
| title_full | Spherical CR geometry and Dehn surgery / Richard Evan Schwartz. |
| title_fullStr | Spherical CR geometry and Dehn surgery / Richard Evan Schwartz. |
| title_full_unstemmed | Spherical CR geometry and Dehn surgery / Richard Evan Schwartz. |
| title_short | Spherical CR geometry and Dehn surgery / |
| title_sort | spherical cr geometry and dehn surgery |
| topic | CR submanifolds. http://id.loc.gov/authorities/subjects/sh85129485 Dehn surgery (Topology) http://id.loc.gov/authorities/subjects/sh2006006222 Three-manifolds (Topology) http://id.loc.gov/authorities/subjects/sh85135028 CR-sous-variétés. Chirurgie de Dehn (Topologie) Variétés topologiques à 3 dimensions. MATHEMATICS Geometry Differential. bisacsh CR submanifolds fast Dehn surgery (Topology) fast Three-manifolds (Topology) fast |
| topic_facet | CR submanifolds. Dehn surgery (Topology) Three-manifolds (Topology) CR-sous-variétés. Chirurgie de Dehn (Topologie) Variétés topologiques à 3 dimensions. MATHEMATICS Geometry Differential. CR submanifolds |
| work_keys_str_mv | AT schwartzrichardevan sphericalcrgeometryanddehnsurgery |