Geometric Group Theory Preliminary Version Under revision

Geometric Group Theory Preliminary Version Under revision

Geometric Group Theory Preliminary Version Under revision

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.

This note covers the following
topics: Notation for sets and functions, Basic group theory, The Symmetric
Group, Group actions, Linear groups, Affine Groups, Projective Groups, Finite
linear groups, Abelian Groups, Sylow Theorems and Applications, Solvable and
nilpotent groups, p-groups, a second look, Presentations of Groups, Building new
groups from old.

This note describes
the following topics: Abstract Group Theory, Theory of Group Representations,
Group Theory in Quantum Mechanics, Lie Groups, Atomic Physics, The Group SU2:
Isospin, The Point Groups, The Group SU3.

This note explains the following
topics: Simple groups, Examples of groups, Group actions, Sylow’s Theorem, Group
extensions, Soluble and nilpotent groups, Symmetric and alternating groups,
Linear groups.