03590nam a22005295i 4500 978-3-031-48443-8 DE-He213 20251030112042.0 cr nn 008mamaa 240515s2024 sz | s |||| 0|eng d 9783031484438 978-3-031-48443-8 10.1007/978-3-031-48443-8 doi QA174-183 PBG bicssc MAT002010 bisacsh PBG thema Davis, Michael W. author. aut http://id.loc.gov/vocabulary/relators/aut 76842 Infinite Group Actions on Polyhedra [electronic resource] / by Michael W. Davis. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XI, 271 p. 9 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 2197-5655 ; 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. Group theory. 70149 Polytopes. 76843 Manifolds (Mathematics). 69683 Group Theory and Generalizations. 70154 Polytopes. 76843 Manifolds and Cell Complexes. 73090 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031484421 Printed edition: 9783031484445 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 2197-5655 ; 77 76844 https://doi.org/10.1007/978-3-031-48443-8 ZDB-2-SMA ZDB-2-SXMS 59865 59865