English

An Introduction to Geometric Group Theory

Group Theory 2025-02-11 v2 Geometric Topology Metric Geometry

Abstract

This book provides a self-contained introduction to geometric group theory. The topics range from an introduction of Cayley and Schreier graphs to Gromov's theorem on groups of polynomial growth and amenability. We discuss the ping-pong lemma, quasi-isometries, growth of groups, hyperbolicity, and other related notions. The book is based on graduate courses and can be used for such a course or for independent study.

Keywords

Cite

@article{arxiv.2409.17797,
  title  = {An Introduction to Geometric Group Theory},
  author = {Mikhail Belolipetsky and Gisele Teixeira Paula},
  journal= {arXiv preprint arXiv:2409.17797},
  year   = {2025}
}

Comments

277 pages, in Portuguese language; v2: first revision

R2 v1 2026-06-28T18:58:03.671Z