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Geometric and Cohomological Methods in Group Theory.
An extended tour through a selection of the most important trends in modern geometric group theory.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2009.
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| Colección: | London Mathematical Society Lecture Note Series, 358.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Bridson, Martin R. | |
| 245 | 1 | 0 | |a Geometric and Cohomological Methods in Group Theory. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2009. | ||
| 300 | |a 1 online resource (332 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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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. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 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. | |
| 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. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=399263 |z Texto completo |
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