The Geometry and Topology of Coxeter Groups. (LMS-32) / / Michael Davis.
The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2012] ©2008 |
Year of Publication: | 2012 |
Edition: | Course Book |
Language: | English |
Series: | London Mathematical Society Monographs ;
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Physical Description: | 1 online resource (600 p.) :; 31 line illus. 3 tables. |
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Davis, Michael, author. aut http://id.loc.gov/vocabulary/relators/aut The Geometry and Topology of Coxeter Groups. (LMS-32) / Michael Davis. Course Book Princeton, NJ : Princeton University Press, [2012] ©2008 1 online resource (600 p.) : 31 line illus. 3 tables. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda London Mathematical Society Monographs ; 32 Frontmatter -- Contents -- Preface -- Chapter One. INTRODUCTION AND PREVIEW -- Chapter Two. SOME BASIC NOTIONS IN GEOMETRIC GROUP THEORY -- Chapter Three. COXETER GROUPS -- Chapter Four. MORE COMBINATORIAL THEORY OF COXETER GROUPS -- Chapter Five. THE BASIC CONSTRUCTION -- Chapter Six. GEOMETRIC REFLECTION GROUPS -- Chapter Seven. THE COMPLEX Σ -- Chapter Eight. THE ALGEBRAIC TOPOLOGY OF U AND OF Σ -- Chapter Nine. THE FUNDAMENTAL GROUP AND THE FUNDAMENTAL GROUP AT INFINITY -- Chapter Ten. ACTIONS ON MANIFOLDS -- Chapter Eleven. THE REFLECTION GROUP TRICK -- Chapter Twelve. Σ IS CAT(O): THEOREMS OF GROMOV AND MOUSSONG -- Chapter Thirteen. RIGIDITY -- Chapter Fourteen. FREE QUOTIENTS AND SURFACE SUBGROUPS -- Chapter Fifteen. ANOTHER LOOK AT (CO)HOMOLOGY -- Chapter Sixteen. THE EULER CHARACTERISTIC -- Chapter Seventeen. GROWTH SERIES -- Chapter Eighteen. BUILDINGS -- Chapter Nineteen. HECKE-VON NEUMANN ALGEBRAS -- Chapter Twenty. WEIGHTED L2-(CO)HOMOLOGY -- Appendix A: CELL COMPLEXES -- Appendix B: REGULAR POLYTOPES -- Appendix C: THE CLASSIFICATION OF SPHERICAL AND EUCLIDEAN COXETER GROUPS -- Appendix D: THE GEOMETRIC REPRESENTATION -- Appendix E: COMPLEXES OF GROUPS -- Appendix F: HOMOLOGY AND COHOMOLOGY OF GROUPS -- Appendix G: ALGEBRAIC TOPOLOGY AT INFINITY -- Appendix H: THE NOVIKOV AND BOREL CONJECTURES -- Appendix I: NONPOSITIVE CURVATURE -- Appendix J: L2-(CO)HOMOLOGY -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Coxeter groups. MATHEMATICS / Group Theory. bisacsh Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691131382 https://doi.org/10.1515/9781400845941 https://www.degruyter.com/isbn/9781400845941 Cover https://www.degruyter.com/cover/covers/9781400845941.jpg |
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English |
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Davis, Michael, Davis, Michael, |
spellingShingle |
Davis, Michael, Davis, Michael, The Geometry and Topology of Coxeter Groups. (LMS-32) / London Mathematical Society Monographs ; Frontmatter -- Contents -- Preface -- Chapter One. INTRODUCTION AND PREVIEW -- Chapter Two. SOME BASIC NOTIONS IN GEOMETRIC GROUP THEORY -- Chapter Three. COXETER GROUPS -- Chapter Four. MORE COMBINATORIAL THEORY OF COXETER GROUPS -- Chapter Five. THE BASIC CONSTRUCTION -- Chapter Six. GEOMETRIC REFLECTION GROUPS -- Chapter Seven. THE COMPLEX Σ -- Chapter Eight. THE ALGEBRAIC TOPOLOGY OF U AND OF Σ -- Chapter Nine. THE FUNDAMENTAL GROUP AND THE FUNDAMENTAL GROUP AT INFINITY -- Chapter Ten. ACTIONS ON MANIFOLDS -- Chapter Eleven. THE REFLECTION GROUP TRICK -- Chapter Twelve. Σ IS CAT(O): THEOREMS OF GROMOV AND MOUSSONG -- Chapter Thirteen. RIGIDITY -- Chapter Fourteen. FREE QUOTIENTS AND SURFACE SUBGROUPS -- Chapter Fifteen. ANOTHER LOOK AT (CO)HOMOLOGY -- Chapter Sixteen. THE EULER CHARACTERISTIC -- Chapter Seventeen. GROWTH SERIES -- Chapter Eighteen. BUILDINGS -- Chapter Nineteen. HECKE-VON NEUMANN ALGEBRAS -- Chapter Twenty. WEIGHTED L2-(CO)HOMOLOGY -- Appendix A: CELL COMPLEXES -- Appendix B: REGULAR POLYTOPES -- Appendix C: THE CLASSIFICATION OF SPHERICAL AND EUCLIDEAN COXETER GROUPS -- Appendix D: THE GEOMETRIC REPRESENTATION -- Appendix E: COMPLEXES OF GROUPS -- Appendix F: HOMOLOGY AND COHOMOLOGY OF GROUPS -- Appendix G: ALGEBRAIC TOPOLOGY AT INFINITY -- Appendix H: THE NOVIKOV AND BOREL CONJECTURES -- Appendix I: NONPOSITIVE CURVATURE -- Appendix J: L2-(CO)HOMOLOGY -- Bibliography -- Index |
author_facet |
Davis, Michael, Davis, Michael, |
author_variant |
m d md m d md |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Davis, Michael, |
title |
The Geometry and Topology of Coxeter Groups. (LMS-32) / |
title_full |
The Geometry and Topology of Coxeter Groups. (LMS-32) / Michael Davis. |
title_fullStr |
The Geometry and Topology of Coxeter Groups. (LMS-32) / Michael Davis. |
title_full_unstemmed |
The Geometry and Topology of Coxeter Groups. (LMS-32) / Michael Davis. |
title_auth |
The Geometry and Topology of Coxeter Groups. (LMS-32) / |
title_alt |
Frontmatter -- Contents -- Preface -- Chapter One. INTRODUCTION AND PREVIEW -- Chapter Two. SOME BASIC NOTIONS IN GEOMETRIC GROUP THEORY -- Chapter Three. COXETER GROUPS -- Chapter Four. MORE COMBINATORIAL THEORY OF COXETER GROUPS -- Chapter Five. THE BASIC CONSTRUCTION -- Chapter Six. GEOMETRIC REFLECTION GROUPS -- Chapter Seven. THE COMPLEX Σ -- Chapter Eight. THE ALGEBRAIC TOPOLOGY OF U AND OF Σ -- Chapter Nine. THE FUNDAMENTAL GROUP AND THE FUNDAMENTAL GROUP AT INFINITY -- Chapter Ten. ACTIONS ON MANIFOLDS -- Chapter Eleven. THE REFLECTION GROUP TRICK -- Chapter Twelve. Σ IS CAT(O): THEOREMS OF GROMOV AND MOUSSONG -- Chapter Thirteen. RIGIDITY -- Chapter Fourteen. FREE QUOTIENTS AND SURFACE SUBGROUPS -- Chapter Fifteen. ANOTHER LOOK AT (CO)HOMOLOGY -- Chapter Sixteen. THE EULER CHARACTERISTIC -- Chapter Seventeen. GROWTH SERIES -- Chapter Eighteen. BUILDINGS -- Chapter Nineteen. HECKE-VON NEUMANN ALGEBRAS -- Chapter Twenty. WEIGHTED L2-(CO)HOMOLOGY -- Appendix A: CELL COMPLEXES -- Appendix B: REGULAR POLYTOPES -- Appendix C: THE CLASSIFICATION OF SPHERICAL AND EUCLIDEAN COXETER GROUPS -- Appendix D: THE GEOMETRIC REPRESENTATION -- Appendix E: COMPLEXES OF GROUPS -- Appendix F: HOMOLOGY AND COHOMOLOGY OF GROUPS -- Appendix G: ALGEBRAIC TOPOLOGY AT INFINITY -- Appendix H: THE NOVIKOV AND BOREL CONJECTURES -- Appendix I: NONPOSITIVE CURVATURE -- Appendix J: L2-(CO)HOMOLOGY -- Bibliography -- Index |
title_new |
The Geometry and Topology of Coxeter Groups. (LMS-32) / |
title_sort |
the geometry and topology of coxeter groups. (lms-32) / |
series |
London Mathematical Society Monographs ; |
series2 |
London Mathematical Society Monographs ; |
publisher |
Princeton University Press, |
publishDate |
2012 |
physical |
1 online resource (600 p.) : 31 line illus. 3 tables. Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contents -- Preface -- Chapter One. INTRODUCTION AND PREVIEW -- Chapter Two. SOME BASIC NOTIONS IN GEOMETRIC GROUP THEORY -- Chapter Three. COXETER GROUPS -- Chapter Four. MORE COMBINATORIAL THEORY OF COXETER GROUPS -- Chapter Five. THE BASIC CONSTRUCTION -- Chapter Six. GEOMETRIC REFLECTION GROUPS -- Chapter Seven. THE COMPLEX Σ -- Chapter Eight. THE ALGEBRAIC TOPOLOGY OF U AND OF Σ -- Chapter Nine. THE FUNDAMENTAL GROUP AND THE FUNDAMENTAL GROUP AT INFINITY -- Chapter Ten. ACTIONS ON MANIFOLDS -- Chapter Eleven. THE REFLECTION GROUP TRICK -- Chapter Twelve. Σ IS CAT(O): THEOREMS OF GROMOV AND MOUSSONG -- Chapter Thirteen. RIGIDITY -- Chapter Fourteen. FREE QUOTIENTS AND SURFACE SUBGROUPS -- Chapter Fifteen. ANOTHER LOOK AT (CO)HOMOLOGY -- Chapter Sixteen. THE EULER CHARACTERISTIC -- Chapter Seventeen. GROWTH SERIES -- Chapter Eighteen. BUILDINGS -- Chapter Nineteen. HECKE-VON NEUMANN ALGEBRAS -- Chapter Twenty. WEIGHTED L2-(CO)HOMOLOGY -- Appendix A: CELL COMPLEXES -- Appendix B: REGULAR POLYTOPES -- Appendix C: THE CLASSIFICATION OF SPHERICAL AND EUCLIDEAN COXETER GROUPS -- Appendix D: THE GEOMETRIC REPRESENTATION -- Appendix E: COMPLEXES OF GROUPS -- Appendix F: HOMOLOGY AND COHOMOLOGY OF GROUPS -- Appendix G: ALGEBRAIC TOPOLOGY AT INFINITY -- Appendix H: THE NOVIKOV AND BOREL CONJECTURES -- Appendix I: NONPOSITIVE CURVATURE -- Appendix J: L2-(CO)HOMOLOGY -- Bibliography -- Index |
isbn |
9781400845941 9783110442502 9780691131382 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA183 |
callnumber-sort |
QA 3183 G38 42012 |
url |
https://doi.org/10.1515/9781400845941 https://www.degruyter.com/isbn/9781400845941 https://www.degruyter.com/cover/covers/9781400845941.jpg |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512.2 |
dewey-sort |
3512.2 |
dewey-raw |
512.2 |
dewey-search |
512.2 |
doi_str_mv |
10.1515/9781400845941 |
oclc_num |
979742294 |
work_keys_str_mv |
AT davismichael thegeometryandtopologyofcoxetergroupslms32 AT davismichael geometryandtopologyofcoxetergroupslms32 |
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cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
is_hierarchy_title |
The Geometry and Topology of Coxeter Groups. (LMS-32) / |
container_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
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