User:Jowa fan/Books/Geometric and combinatorial group theory

Geometric and combinatorial group theory

 * Intro
 * Geometric group theory
 * Word problem for groups
 * Conjugacy problem
 * Group isomorphism problem
 * Burnside's problem
 * Bass–Serre theory
 * Small cancellation theory
 * Percolation theory


 * Definitions
 * CW complex
 * Presentation of a group
 * Tietze transformations
 * Nielsen transformation
 * Cayley graph
 * Word metric
 * Hyperbolic group
 * Quasi-isometry
 * Dehn function
 * Growth rate (group theory)
 * Automatic group
 * Free product
 * HNN extension
 * Semidirect product
 * Wreath product
 * Van Kampen diagram
 * Amenable group
 * Følner sequence
 * Graph of groups
 * Train track map
 * Out(Fn)
 * CAT(k) space
 * Polycyclic group


 * Theorems and conjectures
 * Ping-pong lemma
 * Higman's embedding theorem
 * Seifert–van Kampen theorem
 * Tits alternative
 * Kurosh subgroup theorem
 * Stallings theorem about ends of groups
 * Gromov's theorem on groups of polynomial growth
 * Hanna Neumann conjecture
 * Von Neumann conjecture


 * Examples
 * Triangle group
 * (2,3,7) triangle group
 * Thompson groups
 * Grigorchuk group
 * Lamplighter group
 * Baumslag–Solitar group
 * Braid group
 * Artin group
 * Grushko theorem
 * Tarski monster group