Topics in Groups and Geometry

Topics in Groups and Geometry
Author :
Publisher : Springer Nature
Total Pages : 468
Release :
ISBN-10 : 9783030881092
ISBN-13 : 3030881091
Rating : 4/5 (92 Downloads)

Book Synopsis Topics in Groups and Geometry by : Tullio Ceccherini-Silberstein

Download or read book Topics in Groups and Geometry written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2022-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Topics in Groups and Geometry Related Books

Topics in Groups and Geometry
Language: en
Pages: 468
Authors: Tullio Ceccherini-Silberstein
Categories: Mathematics
Type: BOOK - Published: 2022-01-01 - Publisher: Springer Nature

DOWNLOAD EBOOK

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 clas
From Groups to Geometry and Back
Language: en
Pages: 442
Authors: Vaughn Climenhaga
Categories: Mathematics
Type: BOOK - Published: 2017-04-07 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract gro
Topics in Geometric Group Theory
Language: en
Pages: 320
Authors: Pierre de la Harpe
Categories: Education
Type: BOOK - Published: 2000-10-15 - Publisher: University of Chicago Press

DOWNLOAD EBOOK

In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their int
Geometric Group Theory
Language: en
Pages: 390
Authors: Clara Löh
Categories: Mathematics
Type: BOOK - Published: 2017-12-19 - Publisher: Springer

DOWNLOAD EBOOK

Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and gra
The Geometry and Topology of Coxeter Groups
Language: en
Pages: 601
Authors: Michael Davis
Categories: Mathematics
Type: BOOK - Published: 2008 - Publisher: Princeton University Press

DOWNLOAD EBOOK

The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Group