Topics in Geometry of Metric Spaces

Draft chapters of a book on quantitative metric geometry will be posted below (last update: May 2015).

Please send comments and corrections to Florent Baudier.

The table of contents contains more indication about the material that will be presented in the different chapters.

Please send comments and corrections to Florent Baudier.

The table of contents contains more indication about the material that will be presented in the different chapters.

Table of contents

Preface

Introduction

Chapter 0. Metric faithfulness: from the origins to modern applications

Preface

Introduction

Chapter 0. Metric faithfulness: from the origins to modern applications

Part I. Lipschitz Geometry

Chapter 1. Metric invariants

Chapter 2. Low distortion embeddings into low dimensional spaces

Chapter 3. Trees and ultrametric spaces

Chapter 4. Embeddability of infinite spaces

Chapter 5. Metric characterizations of spaces with small slicing indices

Chapter 2. Low distortion embeddings into low dimensional spaces

Chapter 3. Trees and ultrametric spaces

Chapter 4. Embeddability of infinite spaces

Chapter 5. Metric characterizations of spaces with small slicing indices

Part II. Small Scale Geometry and Large Scale Geometry

Chapter 6. Embeddings preserving the small and large scale geometries simultaneously

Chapter 7. Uniform and coarse embeddability of metric spaces

Chapter 8. Large scale geometry of metric spaces

Chapter 9. Metric geometry of topological groups

Chapter 7. Uniform and coarse embeddability of metric spaces

Chapter 8. Large scale geometry of metric spaces

Chapter 9. Metric geometry of topological groups

Part III. Large Scale Geometry of Finitely Generated Groups

Chapter 10. Equivariant large scale geometry of finitely generated groups

Chapter 11. Hyperbolic groups

Chapter 12. The Heisenberg group

Chapter 13. Thompson's group F

Chapter 14. Lamplighter groups

Chapter 15. Baumslag-Solitar groups

Chapter 11. Hyperbolic groups

Chapter 12. The Heisenberg group

Chapter 13. Thompson's group F

Chapter 14. Lamplighter groups

Chapter 15. Baumslag-Solitar groups

Appendices

Appendix A. Elements of topology

Appendix B. Elements of graph theory

Appendix C. Elements of group theory

Appendix D. Probabilistic tools

Appendix E. Tools from nonstandard analysis

Appendix F. Basic concepts from Banach space theory

Appendix G. Combinatorial tools

Appendix H. Rudiments of computational complexity

Appendix B. Elements of graph theory

Appendix C. Elements of group theory

Appendix D. Probabilistic tools

Appendix E. Tools from nonstandard analysis

Appendix F. Basic concepts from Banach space theory

Appendix G. Combinatorial tools

Appendix H. Rudiments of computational complexity

Bibliography