The geometry and topology of coxeter groups /:
"The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidea...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton :
Princeton University Press,
©2008.
|
| Schriftenreihe: | London Mathematical Society monographs ;
new ser., no. 32. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book."--Jacket |
| Beschreibung: | Series numbering from spine. |
| Beschreibung: | 1 online resource (xiv, 584 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 555-572) and index. |
| ISBN: | 9781400845941 1400845947 1283851288 9781283851282 |
Internformat
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| 245 | 1 | 4 | |a The geometry and topology of coxeter groups / |c Michael W. Davis. |
| 260 | |a Princeton : |b Princeton University Press, |c ©2008. | ||
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| 490 | 1 | |a London Mathematical Society monographs series ; |v 32 | |
| 500 | |a Series numbering from spine. | ||
| 504 | |a Includes bibliographical references (pages 555-572) and index. | ||
| 520 | 1 | |a "The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book."--Jacket | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Contents; Preface; Chapter 1 INTRODUCTION AND PREVIEW; 1.1 Introduction; 1.2 A Preview of the Right-Angled Case; Chapter 2 SOME BASIC NOTIONS IN GEOMETRIC GROUP THEORY; 2.1 Cayley Graphs and Word Metrics; 2.2 Cayley 2-Complexes; 2.3 Background on Aspherical Spaces; Chapter 3 COXETER GROUPS; 3.1 Dihedral Groups; 3.2 Reflection Systems; 3.3 Coxeter Systems; 3.4 The Word Problem; 3.5 Coxeter Diagrams; Chapter 4 MORE COMBINATORIAL THEORY OF COXETER GROUPS; 4.1 Special Subgroups in Coxeter Groups; 4.2 Reflections; 4.3 The Shortest Element in a Special Coset | |
| 505 | 8 | |a 4.4 Another Characterization of Coxeter Groups4.5 Convex Subsets of W; 4.6 The Element of Longest Length; 4.7 The Letters with Which a Reduced Expression Can End; 4.8 A Lemma of Tits; 4.9 Subgroups Generated by Reflections; 4.10 Normalizers of Special Subgroups; Chapter 5 THE BASIC CONSTRUCTION; 5.1 The Space U; 5.2 The Case of a Pre-Coxeter System; 5.3 Sectors in U; Chapter 6 GEOMETRIC REFLECTION GROUPS; 6.1 Linear Reflections; 6.2 Spaces of Constant Curvature; 6.3 Polytopes with Nonobtuse Dihedral Angles; 6.4 The Developing Map; 6.5 Polygon Groups | |
| 546 | |a English. | ||
| 650 | 0 | |a Coxeter groups. |0 http://id.loc.gov/authorities/subjects/sh00000209 | |
| 650 | 0 | |a Geometric group theory. |0 http://id.loc.gov/authorities/subjects/sh92001537 | |
| 650 | 6 | |a Groupes de Coxeter. | |
| 650 | 6 | |a Théorie géométrique des groupes. | |
| 650 | 7 | |a MATHEMATICS |x Group Theory. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x General. |2 bisacsh | |
| 650 | 7 | |a Coxeter groups |2 fast | |
| 650 | 7 | |a Geometric group theory |2 fast | |
| 650 | 7 | |a Coxeter-Gruppe |2 gnd |0 http://d-nb.info/gnd/4261522-7 | |
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| author | Davis, Michael, 1949 April 26- |
| author_GND | http://id.loc.gov/authorities/names/n78007361 |
| author_facet | Davis, Michael, 1949 April 26- |
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| classification_rvk | SK 260 |
| collection | ZDB-4-EBA |
| contents | Cover; Contents; Preface; Chapter 1 INTRODUCTION AND PREVIEW; 1.1 Introduction; 1.2 A Preview of the Right-Angled Case; Chapter 2 SOME BASIC NOTIONS IN GEOMETRIC GROUP THEORY; 2.1 Cayley Graphs and Word Metrics; 2.2 Cayley 2-Complexes; 2.3 Background on Aspherical Spaces; Chapter 3 COXETER GROUPS; 3.1 Dihedral Groups; 3.2 Reflection Systems; 3.3 Coxeter Systems; 3.4 The Word Problem; 3.5 Coxeter Diagrams; Chapter 4 MORE COMBINATORIAL THEORY OF COXETER GROUPS; 4.1 Special Subgroups in Coxeter Groups; 4.2 Reflections; 4.3 The Shortest Element in a Special Coset 4.4 Another Characterization of Coxeter Groups4.5 Convex Subsets of W; 4.6 The Element of Longest Length; 4.7 The Letters with Which a Reduced Expression Can End; 4.8 A Lemma of Tits; 4.9 Subgroups Generated by Reflections; 4.10 Normalizers of Special Subgroups; Chapter 5 THE BASIC CONSTRUCTION; 5.1 The Space U; 5.2 The Case of a Pre-Coxeter System; 5.3 Sectors in U; Chapter 6 GEOMETRIC REFLECTION GROUPS; 6.1 Linear Reflections; 6.2 Spaces of Constant Curvature; 6.3 Polytopes with Nonobtuse Dihedral Angles; 6.4 The Developing Map; 6.5 Polygon Groups |
| ctrlnum | (OCoLC)823170151 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. 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| id | ZDB-4-EBA-ocn823170151 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:21:11Z |
| institution | BVB |
| isbn | 9781400845941 1400845947 1283851288 9781283851282 |
| language | English |
| oclc_num | 823170151 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xiv, 584 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Princeton University Press, |
| record_format | marc |
| series | London Mathematical Society monographs ; |
| series2 | London Mathematical Society monographs series ; |
| spelling | Davis, Michael, 1949 April 26- https://id.oclc.org/worldcat/entity/E39PCjybHcVTrgHrfh9txQ66gC http://id.loc.gov/authorities/names/n78007361 The geometry and topology of coxeter groups / Michael W. Davis. Princeton : Princeton University Press, ©2008. 1 online resource (xiv, 584 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society monographs series ; 32 Series numbering from spine. Includes bibliographical references (pages 555-572) and index. "The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book."--Jacket Print version record. Cover; Contents; Preface; Chapter 1 INTRODUCTION AND PREVIEW; 1.1 Introduction; 1.2 A Preview of the Right-Angled Case; Chapter 2 SOME BASIC NOTIONS IN GEOMETRIC GROUP THEORY; 2.1 Cayley Graphs and Word Metrics; 2.2 Cayley 2-Complexes; 2.3 Background on Aspherical Spaces; Chapter 3 COXETER GROUPS; 3.1 Dihedral Groups; 3.2 Reflection Systems; 3.3 Coxeter Systems; 3.4 The Word Problem; 3.5 Coxeter Diagrams; Chapter 4 MORE COMBINATORIAL THEORY OF COXETER GROUPS; 4.1 Special Subgroups in Coxeter Groups; 4.2 Reflections; 4.3 The Shortest Element in a Special Coset 4.4 Another Characterization of Coxeter Groups4.5 Convex Subsets of W; 4.6 The Element of Longest Length; 4.7 The Letters with Which a Reduced Expression Can End; 4.8 A Lemma of Tits; 4.9 Subgroups Generated by Reflections; 4.10 Normalizers of Special Subgroups; Chapter 5 THE BASIC CONSTRUCTION; 5.1 The Space U; 5.2 The Case of a Pre-Coxeter System; 5.3 Sectors in U; Chapter 6 GEOMETRIC REFLECTION GROUPS; 6.1 Linear Reflections; 6.2 Spaces of Constant Curvature; 6.3 Polytopes with Nonobtuse Dihedral Angles; 6.4 The Developing Map; 6.5 Polygon Groups English. Coxeter groups. http://id.loc.gov/authorities/subjects/sh00000209 Geometric group theory. http://id.loc.gov/authorities/subjects/sh92001537 Groupes de Coxeter. Théorie géométrique des groupes. MATHEMATICS Group Theory. bisacsh MATHEMATICS Geometry General. bisacsh Coxeter groups fast Geometric group theory fast Coxeter-Gruppe gnd http://d-nb.info/gnd/4261522-7 has work: The geometry and topology of coxeter groups (Text) https://id.oclc.org/worldcat/entity/E39PCFvgRfmYHFR63XYQG3qtgC https://id.oclc.org/worldcat/ontology/hasWork Print version: Davis, Michael, 1949 April 26- Geometry and topology of coxeter groups. Princeton : Princeton University Press, ©2008 9780691131382 (DLC) 2006052879 (OCoLC)77485786 London Mathematical Society monographs ; new ser., no. 32. http://id.loc.gov/authorities/names/n86741199 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=507379 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=507379 Volltext |
| spellingShingle | Davis, Michael, 1949 April 26- The geometry and topology of coxeter groups / London Mathematical Society monographs ; Cover; Contents; Preface; Chapter 1 INTRODUCTION AND PREVIEW; 1.1 Introduction; 1.2 A Preview of the Right-Angled Case; Chapter 2 SOME BASIC NOTIONS IN GEOMETRIC GROUP THEORY; 2.1 Cayley Graphs and Word Metrics; 2.2 Cayley 2-Complexes; 2.3 Background on Aspherical Spaces; Chapter 3 COXETER GROUPS; 3.1 Dihedral Groups; 3.2 Reflection Systems; 3.3 Coxeter Systems; 3.4 The Word Problem; 3.5 Coxeter Diagrams; Chapter 4 MORE COMBINATORIAL THEORY OF COXETER GROUPS; 4.1 Special Subgroups in Coxeter Groups; 4.2 Reflections; 4.3 The Shortest Element in a Special Coset 4.4 Another Characterization of Coxeter Groups4.5 Convex Subsets of W; 4.6 The Element of Longest Length; 4.7 The Letters with Which a Reduced Expression Can End; 4.8 A Lemma of Tits; 4.9 Subgroups Generated by Reflections; 4.10 Normalizers of Special Subgroups; Chapter 5 THE BASIC CONSTRUCTION; 5.1 The Space U; 5.2 The Case of a Pre-Coxeter System; 5.3 Sectors in U; Chapter 6 GEOMETRIC REFLECTION GROUPS; 6.1 Linear Reflections; 6.2 Spaces of Constant Curvature; 6.3 Polytopes with Nonobtuse Dihedral Angles; 6.4 The Developing Map; 6.5 Polygon Groups Coxeter groups. http://id.loc.gov/authorities/subjects/sh00000209 Geometric group theory. http://id.loc.gov/authorities/subjects/sh92001537 Groupes de Coxeter. Théorie géométrique des groupes. MATHEMATICS Group Theory. bisacsh MATHEMATICS Geometry General. bisacsh Coxeter groups fast Geometric group theory fast Coxeter-Gruppe gnd http://d-nb.info/gnd/4261522-7 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh00000209 http://id.loc.gov/authorities/subjects/sh92001537 http://d-nb.info/gnd/4261522-7 |
| title | The geometry and topology of coxeter groups / |
| title_auth | The geometry and topology of coxeter groups / |
| title_exact_search | The geometry and topology of coxeter groups / |
| title_full | The geometry and topology of coxeter groups / Michael W. Davis. |
| title_fullStr | The geometry and topology of coxeter groups / Michael W. Davis. |
| title_full_unstemmed | The geometry and topology of coxeter groups / Michael W. Davis. |
| title_short | The geometry and topology of coxeter groups / |
| title_sort | geometry and topology of coxeter groups |
| topic | Coxeter groups. http://id.loc.gov/authorities/subjects/sh00000209 Geometric group theory. http://id.loc.gov/authorities/subjects/sh92001537 Groupes de Coxeter. Théorie géométrique des groupes. MATHEMATICS Group Theory. bisacsh MATHEMATICS Geometry General. bisacsh Coxeter groups fast Geometric group theory fast Coxeter-Gruppe gnd http://d-nb.info/gnd/4261522-7 |
| topic_facet | Coxeter groups. Geometric group theory. Groupes de Coxeter. Théorie géométrique des groupes. MATHEMATICS Group Theory. MATHEMATICS Geometry General. Coxeter groups Geometric group theory Coxeter-Gruppe |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=507379 |
| work_keys_str_mv | AT davismichael thegeometryandtopologyofcoxetergroups AT davismichael geometryandtopologyofcoxetergroups |