Discrete groups in space and uniformization problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1991
|
| Series: | Mathematics and its applications / Soviet series
40 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | XVII, 482 S. graph. Darst. |
| ISBN: | 0792302168 |
Staff View
MARC
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| 245 | 1 | 0 | |a Discrete groups in space and uniformization problems |c by Boris N. Apanasov |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1991 | |
| 300 | |a XVII, 482 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematics and its applications / Soviet series |v 40 | |
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| 650 | 4 | |a Groupe Möbius | |
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| 650 | 4 | |a Groupe fuchsien | |
| 650 | 4 | |a Isométrie hyperbolique | |
| 650 | 7 | |a Transformations, groupes de |2 ram | |
| 650 | 4 | |a Uniformisation | |
| 650 | 4 | |a Variété Klein | |
| 650 | 4 | |a Conformal mapping | |
| 650 | 4 | |a Transformation groups | |
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Record in the Search Index
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CONTENTS
Series Editor's Preface vii
Preface to the English edition xiii
From the Preface to the Russian edition . xv
Acknowledgements . xvii
Chapter 1. Conformal mappings . 1
§1. Riemannian metric . 1
§2. Quasi conformal mappings and isometry . 2
§3. Mobius transformations . 4
1. Stereographic projection
2. Reflections with respect to spheres and planes
3. Liouvilie's theorem
4. Isometric spheres of Mobius transformations
§4. Automorphisms of a ball and half space . 11
1. Half space automorphisms
2. Automorphisms of the ball
§5. Fixed points of Mobius transformations . . 15
§6. Invariant domains for Mobius subgroups . . 16
Chapter 2. Geometrical structures on manifolds . 19
§1. Fundamental groups and coverings . 19
1. Homotopy equivalence
2. Fundamental group
3. Coverings
§2. Homology and Mayer Vietoris sequences . 22
1. Singular homology
2. Exact sequences
3. Mayer Vietoris sequences
§3. Spaces of constant curvature . 26
1. Elliptic space
2. Hyperbolic space
3. Hemisphere of imaginary radius
4. The projective model of hyperbolic space
5. Lower hemisphere
6. Poincare model in a ball
x CONTENTS
7. Poincare model in the half space RV
8. Spheres and horospheres in the hyperbolic space
§4. Representation of the Mobius group in the matrix group 32
§5. ^ structures in manifolds . 34
§6. Developing map and holonomy . 41
§7. Orbifolds and their ^ structures . 43
Chapter 3. General properties of discontinuous groups . 51
§1. Basic concepts; elementary groups . 51
1. Basic definitions
2. Elementary groups
§2. Action of a group on the discontinuity set . . 54
§3. Some classes of Kleinian groups . 61
1. Fuchsian groups
2. Quasi Fuchsian groups
3. Schottky groups
4. Web groups
5. Degenerate groups
6. Function groups
§4. Fundamental domains . 64
§5. The limit set: the non measurability effect and
density property . 73
Chapter 4. Discrete groups of hyperbolic isometries . . 77
§1. Hyperbolicity and discreteness conditions for a
Mobius group . 77
§2. Arithmetic construction of co compact hyperbolic
groups . 85
§3. Universal bounds of hyperbolic manifold sizes . 87
§4. Margulis lemma and hyperbolic manifold decomposition 93
§5. Precisely invariant horoballs and parabolic Q peaks 101
1. Action of a discrete group in horoballs
2. Parabolic fl peaks and horoball parametrization
§6. Crystallographic reflection groups and arithmetic 109
Chapter 5. Geometrically finite discrete Mobius groups . 117
§1. Local finiteness 117
§2. The convex Nielsen hull of the limit set . . 122
§3. The limit set of a geometrically finite group . 126
§4. Finiteness theorems for discrete Mobius groups . 141
1. Finiteness in the plane
2. Finiteness in space
§5. Invariant components for geometrically finite
Kleinian groups . 154
§6. The geometry of the Nielsen hull boundary . . 168
CONTENTS xi
Chapter 6. Geometric and algebraic structures of discrete
groups igi
§1. Discrete groups and geometry of spatial tessellations 191
1. A filling of the space X"
2. Incomplete fillings of the hyperbolic space
3. Locally finite fillings and completeness of
hyperbolic structures
4. Regular tessellations in the hyperbolic space
5. Rigidity of tessellations in H" for n*4
§2. Free amalgamated products of Kleinian groups . 204
§3. HNN extensions of Kleinian groups. Examples . 212
§4. Cayley graph and combinatorial structure of a
discrete group . 223
1. Visual boundary of the group G
2. Commensurable metrics
3. Group boundary and the limit set
4. Applications to algorithmic problems
§5. Geometric and algebraic convergence of groups . 236
§6. The limit set: Sullivan's ergodic theorems . 241
1. Infinite solid angle of the orbit and ergodicity
2. Conical approximation
3. Horospherical limiit points and conservative
action
Chapter 7. Kleinian manifolds 251
§1. Topological methods 251
§2. Topological aspects of combination theorems . 259
1. Free products
2. Free products with amalgamated cyclic subgroups
3. Double of the manifold M(G) with respect to
the boundary dtf(G)
§3. Kleinian manifold of a function group . . . 263
1. Three dimensional manifolds
2. Multi dimensional Kleinian manifolds
3. Non trivial four dimensional cobordisms having
geometrically finite hyperbolic structures
4. Block building construction
§4. Isomorphism theorems . 283
§5. Geometrically tame ends, Kleinian manifold
compact ification and the Ahlfors problem on limit set
measure . 290
Chapter 8. Uniformization of manifolds . 307
§1. The classical approach . 307
§2. Gromov's and Thurston's geometric uniformization
concepts . 310
1. Length spaces and convexity
2. Thurston's structural conjecture
xi i CONTENTS
§3. Thurston's hyperbolization theorem and the volumes of
hyperbolic manifolds . 318
§4. Complexity of 3 manifolds, integrable Hamiltonian
systems and hyperbolic volumes . 328
1. The Hamiltonian systems and the class (H)
2. The complexity of three dimensional manifolds
3. Computation of volumes of hyperbolic
3 manifolds
§5. Conformal uniformization of manifolds . . . 333
§6. Conformal uniformization of doubles of atoroidal
manifolds . 344
Chapter 9. Deformation spaces of groups and structures . 355
§1. Deformations of locally homogeneous structures . 355
1. Marked locally homogeneous structures
2. Teichmuller space of a Riemann surface
3. Stable representations and the holonomy theorem
4. Infinitesimal deformations and obstructions
§2. Rigidity theorems for complete hyperbolic structures
and isometry groups . 365
1. Finite hyperbolic volume case
2. Infinite volume hyperbolic structures
3. Rigidity of manifolds with boundary
§3. Deformation space for a Fuchsian group . . 381
1. Teichmuller space T(G) of a Fuchsian group in
the plane
2. The space Tn(G) of conjugacy classes of quasi
Fuchsian representations
3. Properties of the space Tn(G): polyhedral
point of view
4. Properties of the space Tn(G) defined by the
geometry of the orbifold HnG
5. Infinitesimal deformations for bendings and
singularities of the spaces Rn{G) and Tn(G)
6. Stamping deformations
7. Stamping with torsion along a closed geodesic
§4. The boundary of deformation space for a Fuchsian
group . 409
§5. Deformations of Kleinian groups and conformal
structures . 415
References 425
Index 467 |
| any_adam_object | 1 |
| author | Apanasov, Boris Nikolaevič 1920- |
| author_GND | (DE-588)105576724X |
| author_facet | Apanasov, Boris Nikolaevič 1920- |
| author_role | aut |
| author_sort | Apanasov, Boris Nikolaevič 1920- |
| author_variant | b n a bn bna |
| building | Verbundindex |
| bvnumber | BV004811327 |
| callnumber-first | Q - Science |
| callnumber-label | QA385 |
| callnumber-raw | QA385 |
| callnumber-search | QA385 |
| callnumber-sort | QA 3385 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 350 |
| classification_tum | MAT 203f |
| ctrlnum | (OCoLC)23902188 (DE-599)BVBBV004811327 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004811327 |
| illustrated | Illustrated |
| indexdate | 2024-09-27T08:01:26Z |
| institution | BVB |
| isbn | 0792302168 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002960708 |
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| owner_facet | DE-12 DE-739 DE-91G DE-BY-TUM DE-824 DE-11 DE-188 |
| physical | XVII, 482 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Apanasov, Boris Nikolaevič 1920- Verfasser (DE-588)105576724X aut Diskretnye gruppy preobrazovanij i struktury mnogoobrazij Discrete groups in space and uniformization problems by Boris N. Apanasov Dordrecht u.a. Kluwer Acad. Publ. 1991 XVII, 482 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 40 Aus d. Russ. übers. Application conforme Applications conformes ram Courbure constante Déformation Espace hyperbolique Groupe Klein Groupe Möbius Groupe discontinu Groupe discret Groupe fuchsien Isométrie hyperbolique Transformations, groupes de ram Uniformisation Variété Klein Conformal mapping Transformation groups Transformationsgruppe (DE-588)4127386-2 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Diskrete Gruppe (DE-588)4135541-6 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Uniformisierung (DE-588)4268725-1 gnd rswk-swf Transformationsgruppe (DE-588)4127386-2 s DE-604 Diskrete Gruppe (DE-588)4135541-6 s Mannigfaltigkeit (DE-588)4037379-4 s Uniformisierung (DE-588)4268725-1 s Geometrie (DE-588)4020236-7 s Soviet series Mathematics and its applications 40 (DE-604)BV004708148 40 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002960708&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Apanasov, Boris Nikolaevič 1920- Discrete groups in space and uniformization problems Application conforme Applications conformes ram Courbure constante Déformation Espace hyperbolique Groupe Klein Groupe Möbius Groupe discontinu Groupe discret Groupe fuchsien Isométrie hyperbolique Transformations, groupes de ram Uniformisation Variété Klein Conformal mapping Transformation groups Transformationsgruppe (DE-588)4127386-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Diskrete Gruppe (DE-588)4135541-6 gnd Geometrie (DE-588)4020236-7 gnd Uniformisierung (DE-588)4268725-1 gnd |
| subject_GND | (DE-588)4127386-2 (DE-588)4037379-4 (DE-588)4135541-6 (DE-588)4020236-7 (DE-588)4268725-1 |
| title | Discrete groups in space and uniformization problems |
| title_alt | Diskretnye gruppy preobrazovanij i struktury mnogoobrazij |
| title_auth | Discrete groups in space and uniformization problems |
| title_exact_search | Discrete groups in space and uniformization problems |
| title_full | Discrete groups in space and uniformization problems by Boris N. Apanasov |
| title_fullStr | Discrete groups in space and uniformization problems by Boris N. Apanasov |
| title_full_unstemmed | Discrete groups in space and uniformization problems by Boris N. Apanasov |
| title_short | Discrete groups in space and uniformization problems |
| title_sort | discrete groups in space and uniformization problems |
| topic | Application conforme Applications conformes ram Courbure constante Déformation Espace hyperbolique Groupe Klein Groupe Möbius Groupe discontinu Groupe discret Groupe fuchsien Isométrie hyperbolique Transformations, groupes de ram Uniformisation Variété Klein Conformal mapping Transformation groups Transformationsgruppe (DE-588)4127386-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Diskrete Gruppe (DE-588)4135541-6 gnd Geometrie (DE-588)4020236-7 gnd Uniformisierung (DE-588)4268725-1 gnd |
| topic_facet | Application conforme Applications conformes Courbure constante Déformation Espace hyperbolique Groupe Klein Groupe Möbius Groupe discontinu Groupe discret Groupe fuchsien Isométrie hyperbolique Transformations, groupes de Uniformisation Variété Klein Conformal mapping Transformation groups Transformationsgruppe Mannigfaltigkeit Diskrete Gruppe Geometrie Uniformisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002960708&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
| work_keys_str_mv | AT apanasovborisnikolaevic diskretnyegruppypreobrazovanijistrukturymnogoobrazij AT apanasovborisnikolaevic discretegroupsinspaceanduniformizationproblems |