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Books > Science & Mathematics > Mathematics > Combinatorics & graph theory
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Topics in Groups and Geometry - Growth, Amenability, and Random Walks (Paperback, 1st ed. 2021)
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Topics in Groups and Geometry - Growth, Amenability, and Random Walks (Paperback, 1st ed. 2021)
Series: Springer Monographs in Mathematics
Expected to ship within 12 - 19 working days
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This book provides a detailed exposition of a wide range of topics
in geometric group theory, inspired by Gromov's pivotal work in the
1980s. It includes classical theorems on nilpotent groups and
solvable groups, a fundamental study of the growth of groups, a
detailed look at asymptotic cones, and a discussion of related
subjects including filters and ultrafilters, dimension theory,
hyperbolic geometry, amenability, the Burnside problem, and random
walks on groups. The results are unified under the common theme of
Gromov's theorem, namely that finitely generated groups of
polynomial growth are virtually nilpotent. This beautiful result
gave birth to a fascinating new area of research which is still
active today.The purpose of the book is to collect these naturally
related results together in one place, most of which are scattered
throughout the literature, some of them appearing here in book form
for the first time. In this way, the connections between these
topics are revealed, providing a pleasant introduction to geometric
group theory based on ideas surrounding Gromov's theorem. The book
will be of interest to mature undergraduate and graduate students
in mathematics who are familiar with basic group theory and
topology, and who wish to learn more about geometric, analytic, and
probabilistic aspects of infinite groups.
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