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.
Table of contents
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
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
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
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
Bibliography