Topics in geometric group theory /
vi, 310 p. : ill. ; 24 cm. - (Chicago lectures in mathematics ) Content notes : I. Gauss' circle problem and Polya's random walks on lattices --
The circle problem --
Polya's recurrence theorem --
II. Free products and free groups --
Free Products of Groups --
The Table-Tennis Lemma (Klein's criterion) and examples of free products --
III. Finitely-generated groups --
Finitely-generated and infinitely-generated groups --
Uncountably many groups with two generators (B.H. Neumann's method) --
On groups with two generators --
On finite quotients of the modular group --
IV. Finitely-generated groups viewed as metric spaces --
Word lengths and Cayley graphs --
Quasi-isometries --
V. Finitely-presented groups --
Finitely-presented groups --
The Poincare theorem on fundamental polygons --
On fundamental groups and curvature in Riemannian geometry --
Complement on Gromov's hyperbolic groups --
VI. Growth of finitely-generated groups --
Growth functions and growth series of groups --
Generalities on growth types --
Exponential growth rate and entropy --
VII. Groups of exponential or polynomial growth --
On groups of exponential growth --
On uniformly exponential growth --
On groups of polynomial growth --
Complement on other kinds of growth --
VIII. The first Grigorchuk group --
Rooted d-ary trees and their automorphisms --
The group [Gamma] as an answer to one of Burnside's problems --
On some subgroups of [Gamma] --
Congruence subgroups --
Word problem and non-existence of finite presentations --
Growth --
Exercises and complements--
References--
Index of research problems--
Subject index.
