Lectures on hyperbolic geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1992
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 330 S. graph. Darst. |
| ISBN: | 354055534X 038755534X |
Staff View
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| 100 | 1 | |a Benedetti, Riccardo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lectures on hyperbolic geometry |c Riccardo Benedetti ; Carlo Petronio |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1992 | |
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Record in the Search Index
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| adam_text | Table of Contents
Preface xi
Chapter A.
Hyperbolic Space 1
A.I Models for Hyperbolic Space 1
A.2 Isometries of Hyperbolic Space: Hyperboloid Model 3
A.3 Conformal Geometry 7
A.4 Isometries of Hyperbolic Space: Disc and Half space Models ... 22
A.5 Geodesies, Hyperbolic Subspaces and Miscellaneous Facts .... 25
A.6 Curvature of Hyperbolic Space 37
Chapter B.
Hyperbolic Manifolds
and the Compact Two dimensional Case 45
B.I Hyperbolic, Elliptic and Flat Manifolds 45
B.2 Topology of Compact Oriented Surfaces 55
B.3 Hyperbolic, Elliptic and Flat Surfaces 58
B.4 Teichmiiller Space 61
Chapter C.
The Rigidity Theorem (Compact Case) 83
C.I First Step of the Proof: Extension of Pseudo isometries 84
C.2 Second Step of the Proof: Volume of Ideal Simplices 94
C.3 Gromov Norm of a Compact Manifold 103
C.4 Third Step of the Proof:
the Gromov Norm and the Volume Are Proportional 105
C.5 Conclusion of the Proof, Corollaries and Generalizations .... 121
Chapter D.
Margulis Lemma and its Applications 133
D.I Margulis Lemma 133
viii Table of Contents
D.2 Local Geometry of a Hyperbolic Manifold 140
D.3 Ends of a Hyperbolic Manifold 143
Chapter E.
The Space of Hyperbolic Manifolds
and the Volume Function 159
E.I The Chabauty and the Geometric Topology 160
E.2 Convergence in the Geometric Topology: Opening Cnsps.
The Case of Dimension at least Three 174
E.3 The Case of Dimension Different from Three.
Conclusions and Examples 184
E.4 The Three dimensional Case: Jorgensen s Part of the
So called Jorgensen Thurston Theory 190
E.5 The Three dimensional Case. Thurston s Hyperbolic
Surgery Theorem: Statement and Preliminaries 196
E.5 i Definition and First Properties of 7jj (Non compact
Three manifolds with Triangulation Without Vertices) .... 198
E.5 ii Hyperbolic Structures on an Element of T^
and Realization of the Complete Structure 201
E.5 iii Elements of 7j) and Standard Spines 207
E.5 iv Some Links Whose Complements
are Realized as Elements of Tjj 210
E.6 Proof of Thurston s Hyperbolic Surgery Theorem 223
E.6 i Algebraic Equations of 7i{M)
(Hyperbolic Structures Supported by MeT3) 224
E.6 ii Dimension of H{M): General Case 234
E.6 iii The Case M is Complete Hyperbolic:
the Space of Deformations 251
E.6 iv Completion of the Deformed Hyperbolic
Structures and Conclusion of the Proof 256
E.7 Applications to the Study of the Volume Function and
Complements about Three dimensional Hyperbolic Geometry .... 267
Chapter F.
Bounded Cohomology, a Rough Outline 273
F.I Singular Cohomology 273
F.2 Bounded Singular Cohomology 277
F.3 Flat Fiber Bundles 280
F.4 Euler Class of a Flat Vector Bundle 287
F.5 Flat Vector Bundles on Surfaces and the Milnor Sullivan Theorem 294
Table of Contents ix
F.6 Sullivan s Conjecture and Amenable Groups 303
Subject Index 321
Notation Index 324
References 326
|
| any_adam_object | 1 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:29:39Z |
| institution | BVB |
| isbn | 354055534X 038755534X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003407032 |
| oclc_num | 26012612 |
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| physical | XIV, 330 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Benedetti, Riccardo Verfasser aut Lectures on hyperbolic geometry Riccardo Benedetti ; Carlo Petronio Berlin [u.a.] Springer 1992 XIV, 330 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Géométrie hyperbolique ram Hyperbolische meetkunde gtt Geometry, Hyperbolic Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 s DE-604 Petronio, Carlo Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003407032&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benedetti, Riccardo Petronio, Carlo Lectures on hyperbolic geometry Géométrie hyperbolique ram Hyperbolische meetkunde gtt Geometry, Hyperbolic Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| subject_GND | (DE-588)4161041-6 |
| title | Lectures on hyperbolic geometry |
| title_auth | Lectures on hyperbolic geometry |
| title_exact_search | Lectures on hyperbolic geometry |
| title_full | Lectures on hyperbolic geometry Riccardo Benedetti ; Carlo Petronio |
| title_fullStr | Lectures on hyperbolic geometry Riccardo Benedetti ; Carlo Petronio |
| title_full_unstemmed | Lectures on hyperbolic geometry Riccardo Benedetti ; Carlo Petronio |
| title_short | Lectures on hyperbolic geometry |
| title_sort | lectures on hyperbolic geometry |
| topic | Géométrie hyperbolique ram Hyperbolische meetkunde gtt Geometry, Hyperbolic Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| topic_facet | Géométrie hyperbolique Hyperbolische meetkunde Geometry, Hyperbolic Hyperbolische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003407032&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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