Infinite Group Actions on Polyhedra (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Mode Surveys in Mathematics, 77)

by: Michael W. Davis (Author)

Publisher:
Edition:2024th

Publication Date: June 16, 2024

Language: English

Print Length: 282 pages

ISBN-10: 3031484428

ISBN-13:

Book Description

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 mode 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.
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 mode 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.

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