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Geometric Group Theory (Hardcover)
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Geometric Group Theory (Hardcover)
Series: Colloquium Publications
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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 this book 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.
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