Spherical CR Geometry and Dehn Surgery

Richard Evan Schwartz - Collection Annals of Mathematic Studies

200 pages, parution le 30/03/2007

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Résumé

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 which bound complex hyperbolic orbifolds--the only known examples of closed manifolds that simultaneously have these two kinds of geometric structures. The second is a complete understanding of the structure of complex hyperbolic reflection triangle groups in cases where the angle is small. In an accessible and straightforward manner, Richard Evan Schwartz also presents a large amount of useful information on complex hyperbolic geometry and discrete groups.

Schwartz relies on elementary proofs and avoids quotations of preexisting technical material as much as possible. For this reason, this book will benefit graduate students seeking entry into this emerging area of research, as well as researchers in allied fields such as Kleinian groups and CR geometry.

L'auteur - Richard Evan Schwartz

Richard Evan Schwartz is Professor of Mathematics at Brown University.

Sommaire

Basic Material
- Introduction
- Rank-One Geometry
- Topological Generalities
- Reflection Triangle Groups
- Heuristic Discussion of Geometric Filling
Proof of the Hst
- Extending Horotube Functions
- Transplanting Horotube Functions
- The Local Surgery Formula
- Horotube Assignments
- Constructing the Boundary Complex
- Extending to the Inside
- Machinery for Proving Discreteness
- Proof of the HST
The Applications
- The Convergence Lemmas
- Cusp Flexibility
- CR Surgery on the Whitehead Link Complement
- Covers of the Whitehead Link Complement
- Small-Angle Triangle Groups
Structure of Ideal Triangle Groups
- Some Spherical CR Geometry
- The Golden Triangle Group
- The Manifold at Infinity
- The Groups near the Critical Value
- The Groups far from the Critical Value

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	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	Richard Evan Schwartz
Collection	Annals of Mathematic Studies
Parution	30/03/2007
Nb. de pages	200
Format	15,5 x 23,5
Couverture	Broché
Poids	338g
Intérieur	Noir et Blanc
EAN13	9780691128108
ISBN13	978-0-691-12810-8