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Spherical CR Geometry and Dehn Surgery (AM-165) /
This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds whic...
| Autor principal: | |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2007.
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| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. BASIC MATERIAL; Chapter 1. Introduction; 1.1 Dehn Filling and Thurston's Theorem; 1.2 Definition of a Horotube Group; 1.3 The Horotube Surgery Theorem; 1.4 Reflection Triangle Groups; 1.5 Spherical CR Structures; 1.6 The Goldman-Parker Conjecture; 1.7 Organizational Notes; Chapter 2. Rank-One Geometry; 2.1 Real Hyperbolic Geometry; 2.2 Complex Hyperbolic Geometry; 2.3 The Siegel Domain and Heisenberg Space; 2.4 The Heisenberg Contact Form; 2.5 Some Invariant Functions; 2.6 Some Geometric Objects.
- Chapter 3. Topological Generalities3.1 The Hausdorff Topology; 3.2 Singular Models and Spines; 3.3 A Transversality Result; 3.4 Discrete Groups; 3.5 Geometric Structures; 3.6 Orbifold Fundamental Groups; 3.7 Orbifolds with Boundary; Chapter 4. Reflection Triangle Groups; 4.1 The Real Hyperbolic Case; 4.2 The Action on the Unit Tangent Bundle; 4.3 Fuchsian Triangle Groups; 4.4 Complex Hyperbolic Triangles; 4.5 The Representation Space; 4.6 The Ideal Case; Chapter 5. Heuristic Discussion of Geometric Filling; 5.1 A Dictionary; 5.2 The Tree Example; 5.3 Hyperbolic Case: Before Filling.
- 5.4 Hyperbolic Case: After Filling5.5 Spherical CR Case: Before Filling; 5.6 Spherical CR Case: After Filling; 5.7 The Tree Example Revisited; PART 2. PROOF OF THE HST; Chapter 6. Extending Horotube Functions; 6.1 Statement of Results; 6.2 Proof of the Extension Lemma; 6.3 Proof of the Auxiliary Lemma; Chapter 7. Transplanting Horotube Functions; 7.1 Statement of Results; 7.2 A Toy Case; 7.3 Proof of the Transplant Lemma; Chapter 8. The Local Surgery Formula; 8.1 Statement of Results; 8.2 The Canonical Marking; 8.3 The Homeomorphism; 8.4 The Surgery Formula; Chapter 9. Horotube Assignments.
- 9.1 Basic Definitions9.2 The Main Result; 9.3 Corollaries; Chapter 10. Constructing the Boundary Complex; 10.1 Statement of Results; 10.2 Proof of the Structure Lemma; 10.3 Proof of the Horotube Assignment Lemma; Chapter 11. Extending to the Inside; 11.1 Statement of Results; 11.2 Proof of the Transversality Lemma; 11.3 Proof of the Local Structure Lemma; 11.4 Proof of the Compatibility Lemma; 11.5 Proof of the Finiteness Lemma; Chapter 12. Machinery for Proving Discreteness; 12.1 Chapter Overview; 12.2 Simple Complexes; 12.3 Chunks; 12.4 Geometric Equivalence Relations.
- 12.5 Alignment by a Simple ComplexChapter 13. Proof of the HST; 13.1 The Unperturbed Case; 13.2 The Perturbed Case; 13.3 Defining the Chunks; 13.4 The Discreteness Proof; 13.5 The Surgery Formula; 13.6 Horotube Group Structure; 13.7 Proof of Theorem 1.11; 13.8 Dealing with Elliptics; PART 3. THE APPLICATIONS; Chapter 14. The Convergence Lemmas; 14.1 Statement of Results; 14.2 Preliminary Lemmas; 14.3 Proof of the Convergence Lemma I; 14.4 Proof of the Convergence Lemma II; 14.5 Proof of the Convergence Lemma III; Chapter 15. Cusp Flexibility; 15.1 Statement of Results.