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The Geometry and Topology of Coxeter Groups. (LMS-32).
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton University Press
2012.
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| Colección: | London Mathematical Society monographs.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; 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
- 4.4 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