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arXiv:2409.17797 [math.GR]AbstractReferencesReviewsResources

An Introduction to Geometric Group Theory

Mikhail Belolipetsky, Gisele Teixeira Paula

Published 2024-09-26, updated 2025-02-10Version 2

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.

Comments: 277 pages, in Portuguese language; v2: first revision
Categories: math.GR, math.GT, math.MG
Subjects: 20-01, 20F65, 20F05, 20F67, 20F69
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