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Office Hours with a Geometric Group Theorist (Paperback)
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Office Hours with a Geometric Group Theorist (Paperback)
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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
Poincare, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours
with a Geometric Group Theorist brings together leading experts who
provide one-on-one 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 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,
Office Hours with a Geometric Group Theorist also features numerous
exercises and in-depth projects designed to engage readers and
provide jumping-off points for research projects.
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