Description
Book SynopsisFilling a big gap in the literature, this book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz.
Table of Contents
- Geometry and topology
- Metric spaces
- Differential geometry
- Hyperbolic space
- Groups and their actions
- Median spaces and spaces with measured walls
- Finitely generated and finitely presented groups
- Coarse geometry
- Coarse topology
- Ultralimits of metric spaces
- Gromov-hyperbolic spaces and groups
- Lattices in Lie groups
- Solvable groups
- Geometric aspects of solvable groups
- The Tits alternative
- Gromov's theorem
- The Banach-Tarski paradox
- Amenability and paradoxical decomposition
- Ultralimits, fixed point properties, proper actions
- Stallings's theorem and accessibility
- Proof of Stallings's theorem using harmonic functions
- Quasiconformal mappings
- Groups quasiisometric to $\mathbb{H}^n$
- Quasiisometries of nonuniform lattices in $\mathbb{H}^n$
- A survey of quasiisometric rigidity
- Appendix: Three theorems on linear groups
- Bibliography
- Index
