Geometric and Cohomological Methods in Group Theory.:
An extended tour through a selection of the most important trends in modern geometric group theory.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2009.
|
| Schriftenreihe: | London Mathematical Society Lecture Note Series, 358.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | An extended tour through a selection of the most important trends in modern geometric group theory. |
| Beschreibung: | 8.1 Measure Equivalence and Quasi-Isometry. |
| Beschreibung: | 1 online resource (332 pages) |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9781139116763 1139116762 9781139127424 113912742X 9781139114592 113911459X 9781139107099 1139107097 |
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| 490 | 1 | |a London Mathematical Society Lecture Note Series, 358 ; |v v. 358 | |
| 505 | 0 | |a Cover; Title; Copyright; Contents; Preface; List of Participants; Notes on Sela's work: Limit groups and Makanin-Razborov diagrams; Contents; 1 The Main Theorem; 1.1 Introduction; 1.2 Basic properties of limit groups; 1.3 Modular groups and the statement of the main theorem; 1.4 Makanin-Razborov diagrams; 1.5 Abelian subgroups of limit groups; 1.6 Constructible limit groups; 2 The Main Proposition; 3 Review: Measured laminations and R-tree; 3.1 Laminations; 3.2 Dual trees; 3.3 The structure theorem; 3.4 Spaces of trees; 4 Proof of the Main Proposition; 5 Review: JSJ-theory. | |
| 505 | 8 | |a 6 Limit groups are CLG's7 A more geometric approach; References; Solutions to Bestvina & Feighn's exercises on limit groups; 1 Definitions and elementary properties; 1.1?-residually free groups; 1.2 Limit groups; 1.3 Negative examples; 2 Embeddings in real algebraic groups; 3 GADs for limit groups; 4 Constructible Limit Groups; 4.1 CLGs are CSA; 4.2 Abelian subgroups; 4.3 Heredity; 4.4 Coherence; 4.5 Finite K(G, 1); 4.6 Principal cyclic splittings; 4.7 A criterion in free groups; 4.8 CLGs are limit groups; 5 The Shortening Argument; 5.1 Preliminary ideas; 5.2 The abelian part. | |
| 505 | 8 | |a 5.3 The surface part5.4 The simplicial part; 6 Bestvina and Feighn's geometric approach; 6.1 The space of laminations; 6.2 Matching resolutions in the limit; 6.3 Finding kernel elements carried by leaves; 6.4 Examples of limit groups; References; L2 Invariants from the algebraic point of view; 0 Introduction; Contents; 1 Group von Neumann Algebras; 1.1 The Definition of the Group von Neumann Algebra; 1.2 Ring Theoretic Properties of the Group von Neumann Algebra; 1.3 Dimension Theory over the Group von Neumann Algebra; 2 Definition and Basic Properties of L2-Betti Numbers. | |
| 505 | 8 | |a 2.1 The Definition of L2-Betti Numbers2.2 Basic Properties of L2-Betti Numbers; 2.3 Comparison with Other Definitions; 2.4 L2-Euler Characteristic; 3 Computations of L2-Betti Numbers; 3.1 Abelian Groups; 3.2 Finite Coverings; 3.3 Surfaces; 3.4 Three-Dimensional Manifolds; 3.5 Symmetric Spaces; 3.6 Spaces with S1 Action; 3.7 Mapping Tori; 3.8 Fibrations; 4 The Atiyah Conjecture; 4.1 Reformulations of the Atiyah Conjecture; 4.2 The Ring Theoretic Version of the Atiyah Conjecture; 4.3 The Atiyah Conjecture for Torsion-Free Groups; 4.4 The Atiyah Conjecture Implies the Kaplanski Conjecture. | |
| 505 | 8 | |a 4.5 The Status of the Atiyah Conjecture4.6 Groups Without Bound on the Order of Its Finite Subgroups; 5 Flatness Properties of the Group von Neumann Algebra; 6 Applications to Group Theory; 6.1 L2-Betti Numbers of Groups; 6.2 Vanishing of L2-Betti Numbers of Groups; 6.3 L2-Betti Numbers of Some Specific Groups; 6.4 Deficiency and L2-Betti Numbers of Groups; 7 G- and K-Theory; 7.1 The K0- group of a Group von Neumann Algebra; 7.2 The K1- and L-groups of a Group von Neumann Algebra; 7.3 Applications to G-theory of Group Rings; 7.4 Applications to the Whitehead Group; 8 Measurable Group Theory. | |
| 500 | |a 8.1 Measure Equivalence and Quasi-Isometry. | ||
| 520 | |a An extended tour through a selection of the most important trends in modern geometric group theory. | ||
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Geometric group theory |v Congresses. | |
| 650 | 0 | |a Homology theory |v Congresses. | |
| 650 | 6 | |a Théorie géométrique des groupes |v Congrès. | |
| 650 | 6 | |a Homologie |v Congrès. | |
| 650 | 7 | |a MATHEMATICS |x Group Theory. |2 bisacsh | |
| 650 | 7 | |a Geometric group theory |2 fast | |
| 650 | 7 | |a Homology theory |2 fast | |
| 655 | 7 | |a Conference papers and proceedings |2 fast | |
| 700 | 1 | |a Kropholler, Peter H. | |
| 700 | 1 | |a Leary, Ian J. |0 http://id.loc.gov/authorities/names/no2009188355 | |
| 776 | 0 | 8 | |i Print version: |a Bridson, Martin R. |t Geometric and Cohomological Methods in Group Theory. |d Cambridge : Cambridge University Press, ©2009 |z 9780521757249 |
| 830 | 0 | |a London Mathematical Society Lecture Note Series, 358. | |
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Datensatz im Suchindex
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| _version_ | 1816881780849901568 |
| adam_text | |
| any_adam_object | |
| author | Bridson, Martin R. |
| author2 | Kropholler, Peter H. Leary, Ian J. |
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| author_GND | http://id.loc.gov/authorities/names/no2009188355 |
| author_facet | Bridson, Martin R. Kropholler, Peter H. Leary, Ian J. |
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| building | Verbundindex |
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| callnumber-first | Q - Science |
| callnumber-label | QA183 |
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| callnumber-search | QA183 .G43 2009 |
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| contents | Cover; Title; Copyright; Contents; Preface; List of Participants; Notes on Sela's work: Limit groups and Makanin-Razborov diagrams; Contents; 1 The Main Theorem; 1.1 Introduction; 1.2 Basic properties of limit groups; 1.3 Modular groups and the statement of the main theorem; 1.4 Makanin-Razborov diagrams; 1.5 Abelian subgroups of limit groups; 1.6 Constructible limit groups; 2 The Main Proposition; 3 Review: Measured laminations and R-tree; 3.1 Laminations; 3.2 Dual trees; 3.3 The structure theorem; 3.4 Spaces of trees; 4 Proof of the Main Proposition; 5 Review: JSJ-theory. 6 Limit groups are CLG's7 A more geometric approach; References; Solutions to Bestvina & Feighn's exercises on limit groups; 1 Definitions and elementary properties; 1.1?-residually free groups; 1.2 Limit groups; 1.3 Negative examples; 2 Embeddings in real algebraic groups; 3 GADs for limit groups; 4 Constructible Limit Groups; 4.1 CLGs are CSA; 4.2 Abelian subgroups; 4.3 Heredity; 4.4 Coherence; 4.5 Finite K(G, 1); 4.6 Principal cyclic splittings; 4.7 A criterion in free groups; 4.8 CLGs are limit groups; 5 The Shortening Argument; 5.1 Preliminary ideas; 5.2 The abelian part. 5.3 The surface part5.4 The simplicial part; 6 Bestvina and Feighn's geometric approach; 6.1 The space of laminations; 6.2 Matching resolutions in the limit; 6.3 Finding kernel elements carried by leaves; 6.4 Examples of limit groups; References; L2 Invariants from the algebraic point of view; 0 Introduction; Contents; 1 Group von Neumann Algebras; 1.1 The Definition of the Group von Neumann Algebra; 1.2 Ring Theoretic Properties of the Group von Neumann Algebra; 1.3 Dimension Theory over the Group von Neumann Algebra; 2 Definition and Basic Properties of L2-Betti Numbers. 2.1 The Definition of L2-Betti Numbers2.2 Basic Properties of L2-Betti Numbers; 2.3 Comparison with Other Definitions; 2.4 L2-Euler Characteristic; 3 Computations of L2-Betti Numbers; 3.1 Abelian Groups; 3.2 Finite Coverings; 3.3 Surfaces; 3.4 Three-Dimensional Manifolds; 3.5 Symmetric Spaces; 3.6 Spaces with S1 Action; 3.7 Mapping Tori; 3.8 Fibrations; 4 The Atiyah Conjecture; 4.1 Reformulations of the Atiyah Conjecture; 4.2 The Ring Theoretic Version of the Atiyah Conjecture; 4.3 The Atiyah Conjecture for Torsion-Free Groups; 4.4 The Atiyah Conjecture Implies the Kaplanski Conjecture. 4.5 The Status of the Atiyah Conjecture4.6 Groups Without Bound on the Order of Its Finite Subgroups; 5 Flatness Properties of the Group von Neumann Algebra; 6 Applications to Group Theory; 6.1 L2-Betti Numbers of Groups; 6.2 Vanishing of L2-Betti Numbers of Groups; 6.3 L2-Betti Numbers of Some Specific Groups; 6.4 Deficiency and L2-Betti Numbers of Groups; 7 G- and K-Theory; 7.1 The K0- group of a Group von Neumann Algebra; 7.2 The K1- and L-groups of a Group von Neumann Algebra; 7.3 Applications to G-theory of Group Rings; 7.4 Applications to the Whitehead Group; 8 Measurable Group Theory. |
| ctrlnum | (OCoLC)769341706 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 512/.2 |
| dewey-search | 512.2 512/.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| genre | Conference papers and proceedings fast |
| genre_facet | Conference papers and proceedings |
| id | ZDB-4-EBA-ocn769341706 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:10Z |
| institution | BVB |
| isbn | 9781139116763 1139116762 9781139127424 113912742X 9781139114592 113911459X 9781139107099 1139107097 |
| language | English |
| oclc_num | 769341706 |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (332 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2009 |
| publishDateSearch | 2009 |
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| publisher | Cambridge University Press, |
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| series | London Mathematical Society Lecture Note Series, 358. |
| series2 | London Mathematical Society Lecture Note Series, 358 ; |
| spelling | Bridson, Martin R. Geometric and Cohomological Methods in Group Theory. Cambridge : Cambridge University Press, 2009. 1 online resource (332 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society Lecture Note Series, 358 ; v. 358 Cover; Title; Copyright; Contents; Preface; List of Participants; Notes on Sela's work: Limit groups and Makanin-Razborov diagrams; Contents; 1 The Main Theorem; 1.1 Introduction; 1.2 Basic properties of limit groups; 1.3 Modular groups and the statement of the main theorem; 1.4 Makanin-Razborov diagrams; 1.5 Abelian subgroups of limit groups; 1.6 Constructible limit groups; 2 The Main Proposition; 3 Review: Measured laminations and R-tree; 3.1 Laminations; 3.2 Dual trees; 3.3 The structure theorem; 3.4 Spaces of trees; 4 Proof of the Main Proposition; 5 Review: JSJ-theory. 6 Limit groups are CLG's7 A more geometric approach; References; Solutions to Bestvina & Feighn's exercises on limit groups; 1 Definitions and elementary properties; 1.1?-residually free groups; 1.2 Limit groups; 1.3 Negative examples; 2 Embeddings in real algebraic groups; 3 GADs for limit groups; 4 Constructible Limit Groups; 4.1 CLGs are CSA; 4.2 Abelian subgroups; 4.3 Heredity; 4.4 Coherence; 4.5 Finite K(G, 1); 4.6 Principal cyclic splittings; 4.7 A criterion in free groups; 4.8 CLGs are limit groups; 5 The Shortening Argument; 5.1 Preliminary ideas; 5.2 The abelian part. 5.3 The surface part5.4 The simplicial part; 6 Bestvina and Feighn's geometric approach; 6.1 The space of laminations; 6.2 Matching resolutions in the limit; 6.3 Finding kernel elements carried by leaves; 6.4 Examples of limit groups; References; L2 Invariants from the algebraic point of view; 0 Introduction; Contents; 1 Group von Neumann Algebras; 1.1 The Definition of the Group von Neumann Algebra; 1.2 Ring Theoretic Properties of the Group von Neumann Algebra; 1.3 Dimension Theory over the Group von Neumann Algebra; 2 Definition and Basic Properties of L2-Betti Numbers. 2.1 The Definition of L2-Betti Numbers2.2 Basic Properties of L2-Betti Numbers; 2.3 Comparison with Other Definitions; 2.4 L2-Euler Characteristic; 3 Computations of L2-Betti Numbers; 3.1 Abelian Groups; 3.2 Finite Coverings; 3.3 Surfaces; 3.4 Three-Dimensional Manifolds; 3.5 Symmetric Spaces; 3.6 Spaces with S1 Action; 3.7 Mapping Tori; 3.8 Fibrations; 4 The Atiyah Conjecture; 4.1 Reformulations of the Atiyah Conjecture; 4.2 The Ring Theoretic Version of the Atiyah Conjecture; 4.3 The Atiyah Conjecture for Torsion-Free Groups; 4.4 The Atiyah Conjecture Implies the Kaplanski Conjecture. 4.5 The Status of the Atiyah Conjecture4.6 Groups Without Bound on the Order of Its Finite Subgroups; 5 Flatness Properties of the Group von Neumann Algebra; 6 Applications to Group Theory; 6.1 L2-Betti Numbers of Groups; 6.2 Vanishing of L2-Betti Numbers of Groups; 6.3 L2-Betti Numbers of Some Specific Groups; 6.4 Deficiency and L2-Betti Numbers of Groups; 7 G- and K-Theory; 7.1 The K0- group of a Group von Neumann Algebra; 7.2 The K1- and L-groups of a Group von Neumann Algebra; 7.3 Applications to G-theory of Group Rings; 7.4 Applications to the Whitehead Group; 8 Measurable Group Theory. 8.1 Measure Equivalence and Quasi-Isometry. An extended tour through a selection of the most important trends in modern geometric group theory. Includes bibliographical references. Print version record. Geometric group theory Congresses. Homology theory Congresses. Théorie géométrique des groupes Congrès. Homologie Congrès. MATHEMATICS Group Theory. bisacsh Geometric group theory fast Homology theory fast Conference papers and proceedings fast Kropholler, Peter H. Leary, Ian J. http://id.loc.gov/authorities/names/no2009188355 Print version: Bridson, Martin R. Geometric and Cohomological Methods in Group Theory. Cambridge : Cambridge University Press, ©2009 9780521757249 London Mathematical Society Lecture Note Series, 358. FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=399263 Volltext |
| spellingShingle | Bridson, Martin R. Geometric and Cohomological Methods in Group Theory. London Mathematical Society Lecture Note Series, 358. Cover; Title; Copyright; Contents; Preface; List of Participants; Notes on Sela's work: Limit groups and Makanin-Razborov diagrams; Contents; 1 The Main Theorem; 1.1 Introduction; 1.2 Basic properties of limit groups; 1.3 Modular groups and the statement of the main theorem; 1.4 Makanin-Razborov diagrams; 1.5 Abelian subgroups of limit groups; 1.6 Constructible limit groups; 2 The Main Proposition; 3 Review: Measured laminations and R-tree; 3.1 Laminations; 3.2 Dual trees; 3.3 The structure theorem; 3.4 Spaces of trees; 4 Proof of the Main Proposition; 5 Review: JSJ-theory. 6 Limit groups are CLG's7 A more geometric approach; References; Solutions to Bestvina & Feighn's exercises on limit groups; 1 Definitions and elementary properties; 1.1?-residually free groups; 1.2 Limit groups; 1.3 Negative examples; 2 Embeddings in real algebraic groups; 3 GADs for limit groups; 4 Constructible Limit Groups; 4.1 CLGs are CSA; 4.2 Abelian subgroups; 4.3 Heredity; 4.4 Coherence; 4.5 Finite K(G, 1); 4.6 Principal cyclic splittings; 4.7 A criterion in free groups; 4.8 CLGs are limit groups; 5 The Shortening Argument; 5.1 Preliminary ideas; 5.2 The abelian part. 5.3 The surface part5.4 The simplicial part; 6 Bestvina and Feighn's geometric approach; 6.1 The space of laminations; 6.2 Matching resolutions in the limit; 6.3 Finding kernel elements carried by leaves; 6.4 Examples of limit groups; References; L2 Invariants from the algebraic point of view; 0 Introduction; Contents; 1 Group von Neumann Algebras; 1.1 The Definition of the Group von Neumann Algebra; 1.2 Ring Theoretic Properties of the Group von Neumann Algebra; 1.3 Dimension Theory over the Group von Neumann Algebra; 2 Definition and Basic Properties of L2-Betti Numbers. 2.1 The Definition of L2-Betti Numbers2.2 Basic Properties of L2-Betti Numbers; 2.3 Comparison with Other Definitions; 2.4 L2-Euler Characteristic; 3 Computations of L2-Betti Numbers; 3.1 Abelian Groups; 3.2 Finite Coverings; 3.3 Surfaces; 3.4 Three-Dimensional Manifolds; 3.5 Symmetric Spaces; 3.6 Spaces with S1 Action; 3.7 Mapping Tori; 3.8 Fibrations; 4 The Atiyah Conjecture; 4.1 Reformulations of the Atiyah Conjecture; 4.2 The Ring Theoretic Version of the Atiyah Conjecture; 4.3 The Atiyah Conjecture for Torsion-Free Groups; 4.4 The Atiyah Conjecture Implies the Kaplanski Conjecture. 4.5 The Status of the Atiyah Conjecture4.6 Groups Without Bound on the Order of Its Finite Subgroups; 5 Flatness Properties of the Group von Neumann Algebra; 6 Applications to Group Theory; 6.1 L2-Betti Numbers of Groups; 6.2 Vanishing of L2-Betti Numbers of Groups; 6.3 L2-Betti Numbers of Some Specific Groups; 6.4 Deficiency and L2-Betti Numbers of Groups; 7 G- and K-Theory; 7.1 The K0- group of a Group von Neumann Algebra; 7.2 The K1- and L-groups of a Group von Neumann Algebra; 7.3 Applications to G-theory of Group Rings; 7.4 Applications to the Whitehead Group; 8 Measurable Group Theory. Geometric group theory Congresses. Homology theory Congresses. Théorie géométrique des groupes Congrès. Homologie Congrès. MATHEMATICS Group Theory. bisacsh Geometric group theory fast Homology theory fast |
| title | Geometric and Cohomological Methods in Group Theory. |
| title_auth | Geometric and Cohomological Methods in Group Theory. |
| title_exact_search | Geometric and Cohomological Methods in Group Theory. |
| title_full | Geometric and Cohomological Methods in Group Theory. |
| title_fullStr | Geometric and Cohomological Methods in Group Theory. |
| title_full_unstemmed | Geometric and Cohomological Methods in Group Theory. |
| title_short | Geometric and Cohomological Methods in Group Theory. |
| title_sort | geometric and cohomological methods in group theory |
| topic | Geometric group theory Congresses. Homology theory Congresses. Théorie géométrique des groupes Congrès. Homologie Congrès. MATHEMATICS Group Theory. bisacsh Geometric group theory fast Homology theory fast |
| topic_facet | Geometric group theory Congresses. Homology theory Congresses. Théorie géométrique des groupes Congrès. Homologie Congrès. MATHEMATICS Group Theory. Geometric group theory Homology theory Conference papers and proceedings |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=399263 |
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