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The geometry and topology of coxeter groups /

Michael W. Davis.

Book Cover
Main Author: Davis, Michael
Published: Princeton : Princeton University Press, ©2008.
Series: London Mathematical Society monographs ; new ser., no. 32.
Topics: Coxeter groups. | Geometric group theory. | MATHEMATICS - Group Theory. | MATHEMATICS - Geometry - General. | Coxeter-Gruppe
Genres: Electronic books.
Online Access: JSTOR EBA - Full text online
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100 1 |aDavis, Michael,|d1949 April 26-
245 14|aThe geometry and topology of coxeter groups /|cMichael W. Davis.
260 |aPrinceton :|bPrinceton University Press,|c©2008.
300 |a1 online resource (xiv, 584 pages) :|billustrations.
336 |atext|btxt|2rdacontent
337 |acomputer|bc|2rdamedia
338 |aonline resource|bcr|2rdacarrier
490 1 |aLondon Mathematical Society monographs series ;|v32
500 |aSeries numbering from spine.
504 |aIncludes bibliographical references (pages 555-572) and index.
505 0 |aCover; Contents; Preface; Chapter 1 INTRODUCTION AND PREVIEW; 1.1 Introduction; 1.2 A Preview of the Right-Angled Case; Chapter 2 SOME BASIC NOTIONS IN GEOMETRIC GROUP THEORY; 2.1 Cayley Graphs and Word Metrics; 2.2 Cayley 2-Complexes; 2.3 Background on Aspherical Spaces; Chapter 3 COXETER GROUPS; 3.1 Dihedral Groups; 3.2 Reflection Systems; 3.3 Coxeter Systems; 3.4 The Word Problem; 3.5 Coxeter Diagrams; Chapter 4 MORE COMBINATORIAL THEORY OF COXETER GROUPS; 4.1 Special Subgroups in Coxeter Groups; 4.2 Reflections; 4.3 The Shortest Element in a Special Coset
505 8 |a4.4 Another Characterization of Coxeter Groups4.5 Convex Subsets of W; 4.6 The Element of Longest Length; 4.7 The Letters with Which a Reduced Expression Can End; 4.8 A Lemma of Tits; 4.9 Subgroups Generated by Reflections; 4.10 Normalizers of Special Subgroups; Chapter 5 THE BASIC CONSTRUCTION; 5.1 The Space U; 5.2 The Case of a Pre-Coxeter System; 5.3 Sectors in U; Chapter 6 GEOMETRIC REFLECTION GROUPS; 6.1 Linear Reflections; 6.2 Spaces of Constant Curvature; 6.3 Polytopes with Nonobtuse Dihedral Angles; 6.4 The Developing Map; 6.5 Polygon Groups
520 1 |a"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."--Jacket.
588 0 |aPrint version record.
650 0|aCoxeter groups.
650 0|aGeometric group theory.
650 7|aMATHEMATICS|xGroup Theory.|2bisacsh
650 7|aMATHEMATICS|xGeometry|xGeneral.|2bisacsh
650 7|aCoxeter groups.|2fast|0(OCoLC)fst00882060
650 7|aGeometric group theory.|2fast|0(OCoLC)fst00940833
650 7|aCoxeter-Gruppe|2gnd
655 4|aElectronic books.
776 08|iPrint version:|aDavis, Michael, 1949 April 26-|tGeometry and topology of coxeter groups.|dPrinceton : Princeton University Press, ©2008|z9780691131382|w(DLC) 2006052879|w(OCoLC)77485786
830 0|aLondon Mathematical Society monographs ;|vnew ser., no. 32.
852 8 |beresour-nc|hOnline Resource|t1|zAccessible anywhere on campus or with UIUC NetID
856 40|3JSTOR EBA - Full text online|uhttp://www.library.illinois.edu/proxy/go.php?url=https://www.jstor.org/stable/10.2307/j.ctt1r2fnf
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938 |aProQuest MyiLibrary Digital eBook Collection|bIDEB|ncis24345363
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Staff View for: The geometry and topology of coxeter gro