**Colloquium Publications**

Volume: 63;
2017;
Hardcover

MSC: Primary 20; 57;

Print ISBN: 978-1-4704-1104-6

Product Code: COLL/63

List Price: $135.00

Individual Member Price: $108.00

**Electronic ISBN: 978-1-4704-4164-7
Product Code: COLL/63.E**

List Price: $135.00

Individual Member Price: $108.00

# Geometric Group Theory

Share this page
*Cornelia Druţu; Michael Kapovich*

With an appendix by Bogdan Nica

The key idea in geometric group theory is to
study infinite groups by endowing them with a metric and treating them
as geometric spaces. This applies to many groups naturally appearing
in topology, geometry, and algebra, such as fundamental groups of
manifolds, groups of matrices with integer coefficients, etc. The
primary focus of geometric group theory is to cover the foundations of
geometric group theory, including coarse topology, ultralimits and
asymptotic cones, hyperbolic groups, isoperimetric inequalities,
growth of groups, amenability, Kazhdan's Property (T) and the Haagerup
property, as well as their characterizations in terms of group actions
on median spaces and spaces with walls.

The book contains proofs of several fundamental results of
geometric group theory, such as Gromov's theorem on groups of
polynomial growth, Tits's alternative, Stallings's theorem on ends of
groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem,
and quasiisometric rigidity theorems of Tukia and Schwartz. This is
the first book in which geometric group theory is presented in a form
accessible to advanced graduate students and young research
mathematicians. It fills a big gap in the literature and will be used
by researchers in geometric group theory and its applications.

#### Readership

Graduate students and researchers interested in geometric group theory.