Torsions of 3-dimensional manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel ; Boston ; Berlin
Birkhäuser
2002
|
| Series: | Progress in mathematics
208 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 196 S. 24 cm |
| ISBN: | 3764369116 |
Staff View
MARC
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| 100 | 1 | |a Turaev, Vladimir G. |d 1954- |e Verfasser |0 (DE-588)122717791 |4 aut | |
| 245 | 1 | 0 | |a Torsions of 3-dimensional manifolds |c Vladimir Turaev |
| 264 | 1 | |a Basel ; Boston ; Berlin |b Birkhäuser |c 2002 | |
| 300 | |a X, 196 S. |b 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a Variedades topologicas de dimensão 3 |2 larpcal | |
| 650 | 4 | |a Three-manifolds (Topology) | |
| 650 | 4 | |a Torsion theory (Algebra) | |
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Record in the Search Index
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| adam_text | Contents
Introduction ix
I Generalities on Torsions
1.1 Torsions of chain complexes and CW spaces 1
1.2 Combinatorial Euler structures and their torsions 3
1.3 The maximal abelian torsion 6
1.4 Smooth Euler structures and their torsions 8
II The Torsion versus the Alexander Fox Invariants
II. 1 The first elementary ideal 13
11.2 The case i 2 19
11.3 The case i = 1 22
11.4 Extension to 3 manifolds with boundary 23
11.5 The Alexander polynomials 27
III The Torsion versus the Cohomology Rings
111.1 Determinant and Pfaffian for alternate trilinear forms 31
111.2 The integral cohomology ring 36
111.3 Square volume forms and refined determinants 42
111.4 The cohomology ring mod r 45
IV The Torsion Norm
IV. 1 The torsion polytope and the torsion norm 53
IV.2 Comparison with the Thurston norm 57
IV.3 Proof of Theorem 2.2 59
V Homology Orientations in Dimension Three
V.I Relative torsions of chain complexes 65
V.2 Induced homology orientations 67
V.3 Homology orientations and link exteriors 68
V.4 Homology orientations and surgery 70
VI Euler Structures on 3 manifolds
VI. 1 Gluing of smooth Euler structures and the class c 73
VI.2 Euler structures on solid tori and link exteriors 75
VI.3 Gluing of combinatorial Euler structures and torsions 78
viii Contents
VII A Gluing Formula with Applications
VII.1 A gluing formula 81
VII.2 The Alexander Conway function and surgery 86
VII.3 Proof of Formula (I.4.e) 90
VII.4 The torsion versus the Casson Walker Lescop invariant .... 91
VII.5 Examples and computations 93
VIII Surgery Formulas for Torsions
VIII.l Two lemmas 99
VIII.2 A surgery formula for (^ torsions 102
VIII.3 A surgery formula for the Alexander polynomial 106
VIII.4 A surgery formula for t(M) in the case 6i(M) 1 109
VIII.5 Realization of the torsion 114
IX The Torsion Function
IX. 1 The torsion function, basic Euler structures, and gluing .... 119
IX.2 Moments of the torsion function 123
IX.3 Axioms for the torsion function 126
IX.4 A surgery formula for the torsion function 131
IX.5 Formal expansions in Q(H) with applications 132
X Torsion of Rational Homology Spheres
X.I The torsion and the first elementary ideal 139
X.2 The torsion versus the linking form 142
X.3 The torsion versus the cohomology ring modr 145
X.4 A gluing formula 150
X.5 A surgery formula 153
X.6 The torsion function and its moments 157
XI Spinc Structures
XI. 1 Spinc structures on 3 manifolds 161
XI.2 The torsion function versus the Seiberg Witten invariants . . . 164
XI.3 Spin structures on 3 manifolds 169
XII Miscellaneous
XII. 1 Torsions of connected sums 175
XII.2 The torsion versus the Massey products 177
XII.3 Genus estimates for Zr surfaces 181
Open Problems 187
Bibliography 189
Index 195
|
| any_adam_object | 1 |
| author | Turaev, Vladimir G. 1954- |
| author_GND | (DE-588)122717791 |
| author_facet | Turaev, Vladimir G. 1954- |
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| author_sort | Turaev, Vladimir G. 1954- |
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| building | Verbundindex |
| bvnumber | BV014818319 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 SK 350 |
| ctrlnum | (OCoLC)50866843 (DE-599)BVBBV014818319 |
| dewey-full | 514/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.3 |
| dewey-search | 514/.3 |
| dewey-sort | 3514 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014818319 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:07:34Z |
| institution | BVB |
| isbn | 3764369116 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010027082 |
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| owner_facet | DE-824 DE-355 DE-BY-UBR DE-634 DE-11 DE-188 |
| physical | X, 196 S. 24 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Turaev, Vladimir G. 1954- Verfasser (DE-588)122717791 aut Torsions of 3-dimensional manifolds Vladimir Turaev Basel ; Boston ; Berlin Birkhäuser 2002 X, 196 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 208 Topologia larpcal Variedades diferenciáveis larpcal Variedades topologicas de dimensão 3 larpcal Three-manifolds (Topology) Torsion theory (Algebra) Torsion Mathematik (DE-588)4627078-4 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Topologische Invariante (DE-588)4310559-2 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s Topologische Invariante (DE-588)4310559-2 s Torsion Mathematik (DE-588)4627078-4 s DE-604 Progress in mathematics 208 (DE-604)BV000004120 208 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010027082&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Turaev, Vladimir G. 1954- Torsions of 3-dimensional manifolds Progress in mathematics Topologia larpcal Variedades diferenciáveis larpcal Variedades topologicas de dimensão 3 larpcal Three-manifolds (Topology) Torsion theory (Algebra) Torsion Mathematik (DE-588)4627078-4 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 3 (DE-588)4321722-9 gnd Topologische Invariante (DE-588)4310559-2 gnd |
| subject_GND | (DE-588)4627078-4 (DE-588)4037379-4 (DE-588)4321722-9 (DE-588)4310559-2 |
| title | Torsions of 3-dimensional manifolds |
| title_auth | Torsions of 3-dimensional manifolds |
| title_exact_search | Torsions of 3-dimensional manifolds |
| title_full | Torsions of 3-dimensional manifolds Vladimir Turaev |
| title_fullStr | Torsions of 3-dimensional manifolds Vladimir Turaev |
| title_full_unstemmed | Torsions of 3-dimensional manifolds Vladimir Turaev |
| title_short | Torsions of 3-dimensional manifolds |
| title_sort | torsions of 3 dimensional manifolds |
| topic | Topologia larpcal Variedades diferenciáveis larpcal Variedades topologicas de dimensão 3 larpcal Three-manifolds (Topology) Torsion theory (Algebra) Torsion Mathematik (DE-588)4627078-4 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 3 (DE-588)4321722-9 gnd Topologische Invariante (DE-588)4310559-2 gnd |
| topic_facet | Topologia Variedades diferenciáveis Variedades topologicas de dimensão 3 Three-manifolds (Topology) Torsion theory (Algebra) Torsion Mathematik Mannigfaltigkeit Dimension 3 Topologische Invariante |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010027082&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
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