Link theory in manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Series: | Lecture notes in mathematics
1669 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 167 S. graph. Darst. |
| ISBN: | 3540634355 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
1 Link bordism in manifolds 1
1.1 Definitions and homotopy interpretation 1
1.2 Relative bordism sets 5
1.3 The intersection invariant 6
1.4 The classification theorem 9
1.5 Properties of the intersection map 12
1.6 Elimination of intersections 13
1.7 Realizing intersection invariants 15
1.8 Relations with immersed and embedded link bordism 17
1.9 Examples of the classification 19
2 Enumeration of link bordism in 3 manifolds 21
2.1 Definitions and computation for the ball 21
2.2 The action of the bordism groups of the ball 26
2.3 Classification of oriented bordism 28
2.4 Classification of framed embedded bordism 30
2.5 Interior bordism 34
3 Linking number maps 37
3.1 Linking number maps in abelian groups 37
3.2 The geometric linking number map 43
3.3 Linking number maps in commutative rings 48
3.4 Cyclic ring linking number maps 54
3.5 The universal ring of a Betti trivial 3 manifold 56
3.6 Universal linking numbers and Betti Ik maps 61
4 Surface structures for links in 3 manifolds 69
4.1 Seifert structures 69
4.2 Seifert structures and functorial properties 74
4.3 Band structures, skein relations 79
5 Link invariants in Betti trivial 3 manifolds 85
5.1 Seifert pairings and 5 equivalence 85
5.2 Conway potential and polynomial 89
5.3 Examples 92
5.4 The Conway polynomial and the Conway skein module 96
5.5 More invariants from the Seifert pairing 98
xiv CONTENTS
6 Link characteristic and band operations 99
6.1 Link characteristic 99
6.2 Link characteristic and Conway polynomial 103
6.3 Characteristics of band structures 103
6.4 Generalization of the Scharlemann Thompson theorem 105
6.5 Duality of band operations 107
6.6 Generalizations of the band sum problem 112
7 3 dimensional Betti trivial submanifolds 117
7.1 Planar subsurfaces of oriented surfaces 117
7.2 Full links and some applications 118
7.3 Betti surfaces and capacities 119
7.4 The number of components of Betti surfaces 122
7.5 Construction of Betti surfaces 124
7.6 Cutting complexities 126
7.7 Examples 129
A Appendix 132
A.I Inner homology, Betti numbers and pairings 132
A.2 Submanifolds of rational homology 3 spheres 138
A.3 Homology of link complements in 3 manifolds 142
A.4 Inner Betti numbers of 3 manifolds 154
Bibliography 158
Index 162
Symbol Index 165
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:10:53Z |
| institution | BVB |
| isbn | 3540634355 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007742147 |
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| physical | XIV, 167 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 | Kaiser, Uwe Verfasser aut Link theory in manifolds Uwe Kaiser Berlin [u.a.] Springer 1997 XIV, 167 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1669 Link theory Three-manifolds (Topology) Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Verschlingung (DE-588)4191540-9 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 s Dimension 3 (DE-588)4321722-9 s Verschlingung (DE-588)4191540-9 s DE-604 Lecture notes in mathematics 1669 (DE-604)BV000676446 1669 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007742147&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaiser, Uwe Link theory in manifolds Lecture notes in mathematics Link theory Three-manifolds (Topology) Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Verschlingung (DE-588)4191540-9 gnd Dimension 3 (DE-588)4321722-9 gnd |
| subject_GND | (DE-588)4185712-4 (DE-588)4191540-9 (DE-588)4321722-9 |
| title | Link theory in manifolds |
| title_auth | Link theory in manifolds |
| title_exact_search | Link theory in manifolds |
| title_full | Link theory in manifolds Uwe Kaiser |
| title_fullStr | Link theory in manifolds Uwe Kaiser |
| title_full_unstemmed | Link theory in manifolds Uwe Kaiser |
| title_short | Link theory in manifolds |
| title_sort | link theory in manifolds |
| topic | Link theory Three-manifolds (Topology) Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Verschlingung (DE-588)4191540-9 gnd Dimension 3 (DE-588)4321722-9 gnd |
| topic_facet | Link theory Three-manifolds (Topology) Topologische Mannigfaltigkeit Verschlingung Dimension 3 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007742147&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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