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Infinite group actions on polyhedra

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Infinite group actions on polyhedra/ by Michael W. Davis.
作者:	Davis, Michael W.
出版者:	Cham :Springer International Publishing : : 2024.,
面頁冊數:	xi, 271 p. :ill., digital ;24 cm.
內容註:	Part I: Introduction -- 1 Introduction -- Part II: Nonpositively curved cube complexes -- 2 Polyhedral preliminaries -- 3 Right-angled spaces and groups -- Part III: Coxeter groups, Artin groups, buildings -- 4 Coxeter groups, Artin groups, buildings -- Part IV: More on NPC cube complexes -- 5 General theory of cube complexes -- 6 Hyperbolization -- 7 Morse theory and Bestvina-Brady groups -- Appendix A: Complexes of groups.
Contained By:	Springer Nature eBook
標題:	Infinite groups. -
電子資源:	https://doi.org/10.1007/978-3-031-48443-8
ISBN:	9783031484438

Infinite group actions on polyhedra
Davis, Michael W.

Infinite group actions on polyhedra[electronic resource] /by Michael W. Davis. - Cham :Springer International Publishing :2024. - xi, 271 p. :ill., digital ;24 cm. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,v. 772197-5655 ;. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ;v. 77..

Part I: Introduction -- 1 Introduction -- Part II: Nonpositively curved cube complexes -- 2 Polyhedral preliminaries -- 3 Right-angled spaces and groups -- Part III: Coxeter groups, Artin groups, buildings -- 4 Coxeter groups, Artin groups, buildings -- Part IV: More on NPC cube complexes -- 5 General theory of cube complexes -- 6 Hyperbolization -- 7 Morse theory and Bestvina-Brady groups -- Appendix A: Complexes of groups.

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.

ISBN: 9783031484438

Standard No.: 10.1007/978-3-031-48443-8doiSubjects--Topical Terms:

526101
Infinite groups.

LC Class. No.: QA178

Dewey Class. No.: 512.482

Infinite group actions on polyhedra
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505 0 $a Part I: Introduction -- 1 Introduction -- Part II: Nonpositively curved cube complexes -- 2 Polyhedral preliminaries -- 3 Right-angled spaces and groups -- Part III: Coxeter groups, Artin groups, buildings -- 4 Coxeter groups, Artin groups, buildings -- Part IV: More on NPC cube complexes -- 5 General theory of cube complexes -- 6 Hyperbolization -- 7 Morse theory and Bestvina-Brady groups -- Appendix A: Complexes of groups.
520 $a 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.
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