Topological methods in group theory

Description

Details some of the most recent developments at the interface of topology and geometric group theory. Ideal for graduate students. Cover Series information Title page Copyright information Table of contents List of contributors Preface 1 Left Relatively Convex Subgroups 1.1 Outline 1.2 Left Relatively Convex Subgroups 1.3 Graphs of Groups 1.4 Surface Groups and RAAGs 1.5 Residually Torsion-free Nilpotent Groups and Left Relative Convexity Acknowledgments References 2 Groups with Context-free Co-word Problem and Embeddings into Thompson's Group V 2.1 Introduction 2.2 Background 2.3 Demonstrative Groups 2.4 Main Result Acknowledgments References 4.6 Some QuestionsAcknowledgments References 5 Local Similarity Groups with Context-free Co-word Problem 5.1 Introduction 5.2 Background 5.3 Test Partitions 5.4 A Language for Sim[sub(X)] 5.5 Witness Automata 5.6 Proof of the Main Theorem Acknowledgments References 6 Compacta with Shapes of Finite Complexes: a Direct Approach to the Edwards-Geoghegan-Wall Obstruction 6.1 Introduction 6.2 Background 6.3 Main Results 6.4 Realizing the Obstructions Acknowledgment References 7 The Horofunction Boundary of the Lamplighter Group L[sub(2)] with the Diestel-Leader metric 7.1 Introduction7.2 The Diestel-Leader Metric on L[sub(2)] 7.3 Busemann Points 7.4 Model Horofunctions 7.5 Classification of Horofunctions 7.6 Topology of the Horofunction Boundary 7.7 Action of L[sub(2)] on the Horofunction Boundary Acknowledgments References 8 Intrinsic Geometry of a Euclidean Simplex 8.1 Introduction 8.2 The Main Formula 8.3 The Minimal Allowable Edge Length when all Other Edges have Length 1 8.4 Volume of an n-simplex via Edge Lengths 8.5 Distance from the Barycenter to the Boundary of an Equilateral Simplex