Description 
1 online resource (332 pages) 
Series 
London Mathematical Society Lecture Note Series, 358 ; v. 358 

London Mathematical Society lecture note series ; 358

Contents 
Cover; Title; Copyright; Contents; Preface; List of Participants; Notes on Sela's work: Limit groups and MakaninRazborov 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 MakaninRazborov diagrams; 1.5 Abelian subgroups of limit groups; 1.6 Constructible limit groups; 2 The Main Proposition; 3 Review: Measured laminations and Rtree; 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: JSJtheory 

2.1 The Definition of L2Betti Numbers2.2 Basic Properties of L2Betti Numbers; 2.3 Comparison with Other Definitions; 2.4 L2Euler Characteristic; 3 Computations of L2Betti Numbers; 3.1 Abelian Groups; 3.2 Finite Coverings; 3.3 Surfaces; 3.4 ThreeDimensional 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 TorsionFree 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 L2Betti Numbers of Groups; 6.2 Vanishing of L2Betti Numbers of Groups; 6.3 L2Betti Numbers of Some Specific Groups; 6.4 Deficiency and L2Betti Numbers of Groups; 7 G and KTheory; 7.1 The K0 group of a Group von Neumann Algebra; 7.2 The K1 and Lgroups of a Group von Neumann Algebra; 7.3 Applications to Gtheory of Group Rings; 7.4 Applications to the Whitehead Group; 8 Measurable Group Theory 

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 L2Betti Numbers 

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 
Summary 
An extended tour through a selection of the most important trends in modern geometric group theory 
Notes 
8.1 Measure Equivalence and QuasiIsometry 
Bibliography 
Includes bibliographical references 
Notes 
Print version record 
Subject 
Geometric group theory  Congresses.


Homology theory  Congresses.

Genre/Form 
Conference papers and proceedings.


Conference papers and proceedings.

Form 
Electronic book

Author 
Kropholler, Peter H., 1957


Leary, Ian J.

ISBN 
113911459X (electronic bk.) 

1139116762 

113912742X (electronic bk.) 

9781139114592 (electronic bk.) 

9781139116763 

9781139127424 (electronic bk.) 

(paperback) 

(paperback) 
