03375nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202072001500225100008600240245008700326250001800413264007500431300004200506336002600548337002600574338003600600347002400636490012500660505043500785520112601220650002502346650002202371650003602393650004502429650002202474650004102496710003402537773002602571776003602597776003602633830013202669856004602801912001402847912001502861999001702876978-3-031-48443-8DE-He21320251030112042.0cr nn 008mamaa240515s2024    sz |    s    |||| 0|eng d  a97830314844389978-3-031-48443-87 a10.1007/978-3-031-48443-82doi 4aQA174-183 7aPBG2bicssc 7aMAT0020102bisacsh 7aPBG2thema1 aDavis, Michael W.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97684210aInfinite Group Actions on Polyhedrah[electronic resource] /cby Michael W. Davis.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024.  aXI, 271 p. 9 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,x2197-5655 ;v770 aPart 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.  aIn 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. 0aGroup theory.970149 0aPolytopes.976843 0aManifolds (Mathematics).96968314aGroup Theory and Generalizations.97015424aPolytopes.97684324aManifolds and Cell Complexes.9730902 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303148442108iPrinted edition:z9783031484445 0aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,x2197-5655 ;v7797684440uhttps://doi.org/10.1007/978-3-031-48443-8  aZDB-2-SMA  aZDB-2-SXMS  c59865d59865