Casson's invariant for oriented homology 3-spheres: an exposition
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton Univ. Press
1990
|
| Schriftenreihe: | Mathematical notes
36 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 182 S. graph. Darst. |
| ISBN: | 0691085633 |
Internformat
MARC
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| 100 | 1 | |a Akbulut, Selman |d 1949- |e Verfasser |0 (DE-588)113177216 |4 aut | |
| 245 | 1 | 0 | |a Casson's invariant for oriented homology 3-spheres |b an exposition |c by Selman Akbulut and John D. McCarthy |
| 264 | 1 | |a Princeton, NJ |b Princeton Univ. Press |c 1990 | |
| 300 | |a XVIII, 182 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical notes |v 36 | |
| 650 | 7 | |a Invariants |2 ram | |
| 650 | 7 | |a Topologia |2 larpcal | |
| 650 | 7 | |a Variedades de dimensão baixa |2 larpcal | |
| 650 | 7 | |a Variétés topologiques à 3 dimensions |2 ram | |
| 650 | 4 | |a Invariants | |
| 650 | 4 | |a Three-manifolds (Topology) | |
| 650 | 0 | 7 | |a Dimension 3 |0 (DE-588)4321722-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mannigfaltigkeit |0 (DE-588)4037379-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Invariantentheorie |0 (DE-588)4162209-1 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a McCarthy, John D. |e Verfasser |4 aut | |
| 830 | 0 | |a Mathematical notes |v 36 |w (DE-604)BV000003793 |9 36 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-002601993 | ||
Datensatz im Suchindex
| _version_ | 1804118383781740544 |
|---|---|
| adam_text | (v)
Contents
Preface ix
Introduction xi
Chapter I: Representation Spaces
1. The special unitary group SU(2,I)
(a) identification with S3 1
(b) the tangent bundle of S3 TS3 1
(c) the conjugation actions on S3 and TS3 3
(d) the trace and argument maps 8
(e) the unit quaternions Sp(l) and S03 10
(f) the pure unit quaternions S2 12
2. The space of representations of G, H(G)
(a) the functor R 13
(b) the action of S03 on R(G) 13
(c) the algebraic set associated to a set
of generators, S, of G 17
(d) induced polynomials maps 18
(e) the real algebraic structure of fi(G) 19
3. Representations of a free group
(a) standard model with respect to a basis 20
(b) the homology of R(G) 21
(c) the tangent bundle of R(G) 25
(d) induced orientations of R(G) via a basis of G 28
Chapter II: Heegard Decompositions and Stable Equivalence
1. Heegard decompositions and models
(a) the standard handlebody W 33
(b) the Heegard model (W,h) 34
(c) Heegard decompositions of a three manifold M3 34
(d) associated presentations of II, and H, 35
(vi)
2. Stable equivalence of Heegard decompositions
(a) stable equivalence of Heegard decompositions 40
(b) Singer s theorem on stable equivalence 41
(c) connected sums of Heegard decompositions 42
(d) the genus one decomposition of S3 (T,,Tj) 44
Chapter III: Representation Spaces Associated to
Heegard Decompositions
1. The diagram of representation spaces
(a) the diagram of representation spaces 47
(b) intersection properties of Q, and Q2 48
2. The boundary nap 3 and induced orientations
(a) the boundary map 3 53
(b) the singular set S 58
(c) induced orientations 59
Chapter IV: Casson s Invariant for Oriented Hoaology
3—spheres
1. Casson s invariant for Heegard decompositions
(a) the intersection products 63
(b) Casson s invariant for Heegard decompositions 65
(c) independence of Heegard decomposition 66
2. Casson s invariant for oriented homology 3 spheres
(a) Casson s invariant for oriented homology 3 spheres .... 79
(vii)
Chapter V: Casson s invariant for knots in hoaology 3 spherea
1. Dehn surgery on knots in homology spheres
(a) Dehn surgery on knots in homology spheres 80
(b) preferred Heegard decompositions for Kn 82
2. Casson s invariant for framed knots
(a) Casson s invariant for framed knots 87
(b) the canonical isotopy 88
(c) the difference cycle 6 94
(d) independence of framing 96
3. Casson s invariant for knots
(a) Casson s invariant for knots 97
4. The difference cycle, 6
(a) identification of representation spaces 98
(b) an equivariant trivialization of Nt 99
(c) collapsing 6 to a cycle in R (K) 100
(d) the cycle «_ in R (K) as a pullback 110
5. Casson s invariant for fibered knots
(a) fibered knots 114
(b) Casson s invariant for fibered knots in homology
3 spheres and Lefschetz numbers 116
(c) fibered knots of genus one 123
6. Dehn surgery on unlinks
(a) Dehn surgery on unlinks 125
(b) preferred Heegard decompositions for surgeries
on boundary links 126
(viii)
7. Casson s invariant for unlinks
(a) Casson s invariant for unlinks X (K,L) 128
(b) triviality for boundary links 128
(c) Casson s invariant for unlinks X (K,C,C) 131
8. Casson s invariant and the Alexander polynomial
(a) the Alexander polynomial Aj((t) 133
(b) the second derivative of Aj((t) 135
(c) Casson s invariant and the Alexander polynomial 142
Chapter VI: The Topology of the Space of Representations
1. the topology of f?f
(a) identification of spaces 150
(b) the topology of R^ 151
2. The action of the Torelli group
(a) the action of the Torelli group 176
(b) triviality on the homology of R^ 178
References 181
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:09:26Z |
| institution | BVB |
| isbn | 0691085633 |
| language | English |
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| physical | XVIII, 182 S. graph. Darst. |
| publishDate | 1990 |
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| publisher | Princeton Univ. Press |
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| series | Mathematical notes |
| series2 | Mathematical notes |
| spelling | Akbulut, Selman 1949- Verfasser (DE-588)113177216 aut Casson's invariant for oriented homology 3-spheres an exposition by Selman Akbulut and John D. McCarthy Princeton, NJ Princeton Univ. Press 1990 XVIII, 182 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical notes 36 Invariants ram Topologia larpcal Variedades de dimensão baixa larpcal Variétés topologiques à 3 dimensions ram Invariants Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Invariantentheorie (DE-588)4162209-1 gnd rswk-swf Homologie (DE-588)4141951-0 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s Invariantentheorie (DE-588)4162209-1 s DE-604 Homologie (DE-588)4141951-0 s McCarthy, John D. Verfasser aut Mathematical notes 36 (DE-604)BV000003793 36 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002601993&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Akbulut, Selman 1949- McCarthy, John D. Casson's invariant for oriented homology 3-spheres an exposition Mathematical notes Invariants ram Topologia larpcal Variedades de dimensão baixa larpcal Variétés topologiques à 3 dimensions ram Invariants Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Invariantentheorie (DE-588)4162209-1 gnd Homologie (DE-588)4141951-0 gnd |
| subject_GND | (DE-588)4321722-9 (DE-588)4037379-4 (DE-588)4162209-1 (DE-588)4141951-0 |
| title | Casson's invariant for oriented homology 3-spheres an exposition |
| title_auth | Casson's invariant for oriented homology 3-spheres an exposition |
| title_exact_search | Casson's invariant for oriented homology 3-spheres an exposition |
| title_full | Casson's invariant for oriented homology 3-spheres an exposition by Selman Akbulut and John D. McCarthy |
| title_fullStr | Casson's invariant for oriented homology 3-spheres an exposition by Selman Akbulut and John D. McCarthy |
| title_full_unstemmed | Casson's invariant for oriented homology 3-spheres an exposition by Selman Akbulut and John D. McCarthy |
| title_short | Casson's invariant for oriented homology 3-spheres |
| title_sort | casson s invariant for oriented homology 3 spheres an exposition |
| title_sub | an exposition |
| topic | Invariants ram Topologia larpcal Variedades de dimensão baixa larpcal Variétés topologiques à 3 dimensions ram Invariants Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Invariantentheorie (DE-588)4162209-1 gnd Homologie (DE-588)4141951-0 gnd |
| topic_facet | Invariants Topologia Variedades de dimensão baixa Variétés topologiques à 3 dimensions Three-manifolds (Topology) Dimension 3 Mannigfaltigkeit Invariantentheorie Homologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002601993&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003793 |
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