Name: Infinite Group Actions on Polyhedra
ISBN: 978-3-031-48442-1

Overview

Authors:

Michael W. Davis ⁰

Michael W. Davis
1. Department of Mathematics, The Ohio State University, Columbus, USA
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Covers the general theory of nonpositively curved cube complexes and special cube complexes of Haglund and Wise
Provides a unified treatment of general Coxeter groups, Artin groups and buildings
Describes the polyhedral product construction, the reflection group trick, and hyperbolization

Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (MATHE3, volume 77)

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Keywords

nonpositively curved polyhedra
cube complexes
CAT (0) cube complex
polyhedral products
simple complexes of groups
Coxeter groups
Artin groups
buildings
Bestvina-Brady groups
hyperbolization
Sageev’s construction
virtually Haken conjecture
hyperbolic 3-manifolds
hyperbolic groups
separable subgroups

About this book

In the past fifteen years, the theory of right-angled Artin groups and special cube complexes has emerged as a central topic in geometric group theory. This monograph provides an account of this theory, along with other modern techniques in geometric group theory.

Structured around the theme of group actions on contractible polyhedra, this book explores two prominent methods for constructing such actions: utilizing the group of deck transformations of the universal cover of a nonpositively curved polyhedron and leveraging the theory of simple complexes of groups. The book presents various approaches to obtaining cubical examples through CAT(0) cube complexes, including the polyhedral product construction, hyperbolization procedures, and the Sageev construction. Moreover, it offers a unified presentation of important non-cubical examples, such as Coxeter groups, Artin groups, and groups that act on buildings.

Designed as a resource for graduate students and researchers specializing in geometric group theory, this book should also be of high interest to mathematicians in related areas, such as 3-manifolds.

Authors and Affiliations

Department of Mathematics, The Ohio State University, Columbus, USA

Michael W. Davis

About the author

Michael Davis received a PhD in mathematics from Princeton University in 1975. He was Professor of Mathematics at Ohio State University for thirty nine years, retiring in 2022 as Professor Emeritus. In 2015 he became a Fellow of the AMS. His research is in geometric group theory and topology. Since 1981 his work has focused on topics related to reflection groups including the construction of new examples of aspherical manifolds and the study of their properties.

Bibliographic Information

Book Title: Infinite Group Actions on Polyhedra
Authors: Michael W. Davis
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Hardcover ISBN: 978-3-031-48442-1Due: 22 July 2024
eBook ISBN: 978-3-031-48443-8Due: 22 July 2024
Series ISSN: 0071-1136
Series E-ISSN: 2197-5655
Edition Number: 1
Number of Pages: X, 212
Number of Illustrations: 9 b/w illustrations

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Infinite Group Actions on Polyhedra