Spherical CR Geometry and Dehn Surgery (AM-165) / / Richard Evan Schwartz.
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...
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2007] ©2007 |
| Year of Publication: | 2007 |
| Edition: | Course Book |
| Language: | English |
| Series: | Annals of Mathematics Studies ;
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Schwartz, Richard Evan, author. aut http://id.loc.gov/vocabulary/relators/aut Spherical CR Geometry and Dehn Surgery (AM-165) / Richard Evan Schwartz. Course Book Princeton, NJ : Princeton University Press, [2007] ©2007 1 online resource (200 p.) : 15 halftones. 9 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 165 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 -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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 "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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) CR submanifolds. Dehn surgery (Topology). Three-manifolds (Topology). MATHEMATICS / Geometry / General. bisacsh 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. Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691128108 https://doi.org/10.1515/9781400837199 https://www.degruyter.com/isbn/9781400837199 Cover https://www.degruyter.com/document/cover/isbn/9781400837199/original |
| language |
English |
| format |
eBook |
| author |
Schwartz, Richard Evan, Schwartz, Richard Evan, |
| spellingShingle |
Schwartz, Richard Evan, Schwartz, Richard Evan, Spherical CR Geometry and Dehn Surgery (AM-165) / Annals of Mathematics Studies ; 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 -- Index |
| author_facet |
Schwartz, Richard Evan, Schwartz, Richard Evan, |
| author_variant |
r e s re res r e s re res |
| author_role |
VerfasserIn VerfasserIn |
| author_sort |
Schwartz, Richard Evan, |
| title |
Spherical CR Geometry and Dehn Surgery (AM-165) / |
| title_full |
Spherical CR Geometry and Dehn Surgery (AM-165) / Richard Evan Schwartz. |
| title_fullStr |
Spherical CR Geometry and Dehn Surgery (AM-165) / Richard Evan Schwartz. |
| title_full_unstemmed |
Spherical CR Geometry and Dehn Surgery (AM-165) / Richard Evan Schwartz. |
| title_auth |
Spherical CR Geometry and Dehn Surgery (AM-165) / |
| title_alt |
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 -- Index |
| title_new |
Spherical CR Geometry and Dehn Surgery (AM-165) / |
| title_sort |
spherical cr geometry and dehn surgery (am-165) / |
| series |
Annals of Mathematics Studies ; |
| series2 |
Annals of Mathematics Studies ; |
| publisher |
Princeton University Press, |
| publishDate |
2007 |
| physical |
1 online resource (200 p.) : 15 halftones. 9 line illus. Issued also in print. |
| edition |
Course Book |
| contents |
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 -- Index |
| isbn |
9781400837199 9783110494914 9783110442502 9780691128108 |
| callnumber-first |
Q - Science |
| callnumber-subject |
QA - Mathematics |
| callnumber-label |
QA1 |
| callnumber-sort |
QA 11 |
| url |
https://doi.org/10.1515/9781400837199 https://www.degruyter.com/isbn/9781400837199 https://www.degruyter.com/document/cover/isbn/9781400837199/original |
| illustrated |
Illustrated |
| dewey-hundreds |
500 - Science |
| dewey-tens |
510 - Mathematics |
| dewey-ones |
516 - Geometry |
| dewey-full |
516.3 516.3/6 516.36 |
| dewey-sort |
3516.3 |
| dewey-raw |
516.3 516.3/6 516.36 |
| dewey-search |
516.3 516.3/6 516.36 |
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10.1515/9781400837199 |
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Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
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Spherical CR Geometry and Dehn Surgery (AM-165) / |
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Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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