Geometric Group Theory Preliminary Version Under revision

Overview & Synopsis

The goal of this book is to present several central topics in geometric
group theory, primarily related to the large scale geometry of infinite groups
and spaces on which such groups act, and to illustrate them with fundamental
theorems such as Gromov�s Theorem on groups of polynomial growth. Topics covered includes: 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, Geometric
aspects of solvable groups, Gromov�s Theorem, Amenability and paradoxical
decomposition, Proof of Stallings� Theorem using harmonic functions.