Office hours with a geometric group theorist - Clay, Matt; Margalit, Dan (New Jersey: Princeton University Press, 2017)
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. [This book] brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics .... 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 ping-pong lemma, and automorphisms of free groups. It goes on to cover several large-scale geometric invariants of groups, including quasi-isometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, right-angled 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, [the book] also features numerous exercises and in-depth projects designed to engage readers and provide jumping-off points for research projects.
Groups / Matt Clay and Dan Margalit -- ...and spaces / Matt Clay and Dan Margalit -- Groups acting on trees / Dan Margalit -- Free groups and folding / Matt Clay -- The ping-pong lemma / Johanna Mangahas -- Automorphisms of free groups / Matt Clay -- Quasi-isometries / Dan Margalit and Anne Thomas -- Dehn functions / Timothy Riley -- Hyperbolic groups / Moon Duchin -- Ends of groups / Nic Koban and John Meier -- Asymptotic dimension / Greg Bell -- Growth of groups / Eric Freden -- Coxeter groups / Adam Piggott -- Right-angled artin groups / Robert W. Bell and Matt Clay -- Lamplighter groups / Jennifer Taback -- Thompson's group / Sean Cleary -- Mapping class groups / Tara Brendle, Leah Childers, and Dan Margalit -- Braids / Aaron Abrams
Includes bibliography and index
Keywords: Geometric Group Theory