
Matt Clay,Dan Margalit

20170711>
Author: Matt Clay,Dan Margalit
Publisher: Princeton University Press
ISBN: 1400885396
Category: Mathematics
Page: 456
View: 1823
Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide oneonone instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors. An essential primer for undergraduates making the leap to graduate work, the book begins with free groups—actions of free groups on trees, algorithmic questions about free groups, the pingpong lemma, and automorphisms of free groups. It goes on to cover several largescale geometric invariants of groups, including quasiisometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, rightangled Artin groups, lamplighter groups, mapping class groups, and braid groups. The tone is conversational throughout, and the instruction is driven by examples. Accessible to students who have taken a first course in abstract algebra, Office Hours with a Geometric Group Theorist also features numerous exercises and indepth projects designed to engage readers and provide jumpingoff points for research projects.