Branched standard spines of 3 manifolds:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Series: | Lecture notes in mathematics
1653 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 132 S. graph. Darst. |
| ISBN: | 3540626271 |
Staff View
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| 245 | 1 | 0 | |a Branched standard spines of 3 manifolds |c Riccardo Benedetti ; Carlo Petronio |
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| 300 | |a VIII, 132 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Motivations, plan and statements 1
1.1 Combinatorial realizations of topological categories 1
1.2 Branched standard spines and an outline of the construction 3
1.3 Graphic encoding 5
1.4 Statements of representation theorems 5
1.5 Existing literature and outline of contents 10
2 A review on standard spines and o graphs 13
2.1 Encoding 3 manifolds by o graphs 13
2.2 Reconstruction of the boundary 17
2.3 Surgery presentation of a mirrored manifold and ideal triangulations . . 20
3 Branched standard spines 23
3.1 Branchings on standard spines 23
3.2 Normal o graphs 26
3.3 Bicoloration of the boundary 28
3.4 Examples and existence results 32
3.5 Matveev Piergallini move on branched spines 37
4 Manifolds with boundary 40
4.1 Oriented branchings and flows 40
4.2 Extending the flow to a closed manifold 45
4.3 Flow preserving calculus: definitions and statements 47
4.4 Branched simple spines 50
4.5 Restoring the standard setting 55
4.6 The MP move which changes the flow 60
5 Combed closed manifolds 64
5.1 Simple vs. standard branched spines 64
5.2 The combed calculus 69
6 More on combings, and the closed calculus 73
6.1 Comparison of vector fields up to homotopy 73
6.2 Pontrjagin moves for vector fields, and complete classification 76
6.3 Combinatorial realization of closed manifolds 81
viii CONTENTS
7 Framed and spin manifolds 85
7.1 The Euler cochain 85
7.2 Framings of closed manifolds 87
7.3 The framing calculus 91
7.4 Spin structures on closed manifolds 94
7.5 The spin calculus 95
8 Branched spines and quantum invariants 98
8.1 More on spin structures 98
8.2 A review of recoupling theory and Reshetikhin Turaev Witten invariants 99
8.3 Turaev Viro invariants 101
8.4 An alternative computation of TV invariants 104
9 Problems and perspectives 108
9.1 Internal questions 108
9.2 Questions on invariants 110
9.3 Questions on geometric structures 116
10 Homology and cohomology computations 121
10.1 Homology, cohomology and duality 121
10.2 More homological invariants 123
10.3 Evenly framed knots in a spin manifold 125
Bibliography 127
Index 131
|
| any_adam_object | 1 |
| author | Benedetti, Riccardo Petronio, Carlo |
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| ctrlnum | (OCoLC)246275175 (DE-599)BVBBV011205617 |
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| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik |
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| id | DE-604.BV011205617 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:05:46Z |
| institution | BVB |
| isbn | 3540626271 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007516213 |
| oclc_num | 246275175 |
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| physical | VIII, 132 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Benedetti, Riccardo Verfasser aut Branched standard spines of 3 manifolds Riccardo Benedetti ; Carlo Petronio Berlin [u.a.] Springer 1997 VIII, 132 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1653 Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 s DE-604 Dimension 3 (DE-588)4321722-9 s Petronio, Carlo Verfasser aut Lecture notes in mathematics 1653 (DE-604)BV000676446 1653 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007516213&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benedetti, Riccardo Petronio, Carlo Branched standard spines of 3 manifolds Lecture notes in mathematics Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd |
| subject_GND | (DE-588)4321722-9 (DE-588)4185712-4 |
| title | Branched standard spines of 3 manifolds |
| title_auth | Branched standard spines of 3 manifolds |
| title_exact_search | Branched standard spines of 3 manifolds |
| title_full | Branched standard spines of 3 manifolds Riccardo Benedetti ; Carlo Petronio |
| title_fullStr | Branched standard spines of 3 manifolds Riccardo Benedetti ; Carlo Petronio |
| title_full_unstemmed | Branched standard spines of 3 manifolds Riccardo Benedetti ; Carlo Petronio |
| title_short | Branched standard spines of 3 manifolds |
| title_sort | branched standard spines of 3 manifolds |
| topic | Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd |
| topic_facet | Three-manifolds (Topology) Dimension 3 Topologische Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007516213&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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