EAN: 9783030881115

TOPICS IN GROUPS AND GEOMETRY - TULLIO CECCHERI...

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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