06568nam 2201873 450 991079174670332120230721012903.01-4008-3719-70-691-12810-310.1515/9781400837199(CKB)2560000000081913(EBL)1693629(SSID)ssj0000693378(PQKBManifestationID)11396781(PQKBTitleCode)TC0000693378(PQKBWorkID)10657483(PQKB)10849233(MiAaPQ)EBC1693629(DE-B1597)446889(OCoLC)979579583(DE-B1597)9781400837199(Au-PeEL)EBL1693629(CaPaEBR)ebr10874632(CaONFJC)MIL612095(OCoLC)880531475(EXLCZ)99256000000008191320060816d2007 uy| 0engur|n|---|||||txtccrSpherical CR geometry and Dehn surgery /Richard Evan SchwartzCourse BookPrinceton :Princeton University Press,2007.1 online resource (199 p.)Annals of mathematics studies ;number 165Description based upon print version of record.0-691-12809-X Includes bibliographical references (pages [181]-184) and index. Frontmatter -- Contents -- Preface -- Part 1. Basic Material -- Part 2. Proof of the HST -- Part 3. The Applications -- Part 4. Structure of Ideal Triangle Groups -- Bibliography -- IndexThis 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 "ations 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.Annals of mathematics studies ;number 165.CR submanifoldsDehn surgery (Topology)Three-manifolds (Topology)Arc (geometry).Automorphism.Ball (mathematics).Bijection.Bump function.CR manifold.Calculation.Canonical basis.Cartesian product.Clifford torus.Combinatorics.Compact space.Conjugacy class.Connected space.Contact geometry.Convex cone.Convex hull.Coprime integers.Coset.Covering space.Dehn surgery.Dense set.Diagram (category theory).Diameter.Diffeomorphism.Differential geometry of surfaces.Discrete group.Double coset.Eigenvalues and eigenvectors.Equation.Equivalence class.Equivalence relation.Euclidean distance.Four-dimensional space.Function (mathematics).Fundamental domain.Geometry and topology.Geometry.Harmonic function.Hexagonal tiling.Holonomy.Homeomorphism.Homology (mathematics).Homotopy.Horosphere.Hyperbolic 3-manifold.Hyperbolic Dehn surgery.Hyperbolic geometry.Hyperbolic manifold.Hyperbolic space.Hyperbolic triangle.Hypersurface.I0.Ideal triangle.Intermediate value theorem.Intersection (set theory).Isometry group.Isometry.Limit point.Limit set.Manifold.Mathematical induction.Metric space.Möbius transformation.Parameter.Parity (mathematics).Partial derivative.Partition of unity.Permutation.Polyhedron.Projection (linear algebra).Projectivization.Quotient space (topology).R-factor (crystallography).Real projective space.Right angle.Sard's theorem.Seifert fiber space.Set (mathematics).Siegel domain.Simply connected space.Solid torus.Special case.Sphere.Stereographic projection.Subgroup.Subsequence.Subset.Tangent space.Tangent vector.Tetrahedron.Theorem.Topology.Torus.Transversality (mathematics).Triangle group.Union (set theory).Unit disk.Unit sphere.Unit tangent bundle.CR submanifolds.Dehn surgery (Topology)Three-manifolds (Topology)516.3/6SK 350rvkSchwartz Richard Evan307636MiAaPQMiAaPQMiAaPQBOOK9910791746703321Spherical CR geometry and Dehn surgery731846UNINA