Invariants for homology 3-spheres:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Series: | Encyclopaedia of mathematical sciences
140 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 223 S. graph. Darst. |
| ISBN: | 3540437967 9783642078491 |
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| 245 | 1 | 0 | |a Invariants for homology 3-spheres |c Nikolai Saveliev |
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Record in the Search Index
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| adam_text | NIKOLAI SAVELIEV INVARIANTS FOR HOMOLOGY 3-SPHERES SPRINGER TABLE OF
CONTENTS 1 HOMOLOGY 3-SPHERES 1 1.1 INTEGRAL HOMOLOGY 3-SPHERES 1 1.1.1
HOMOTOPY 3-SPHERES 1 1.1.2 POINCARE HOMOLOGY SPHERE 1 1.1.3 BRIESKORN
HOMOLOGY SPHERES 2 1.1.4 SEIFERT FIBERED HOMOLOGY SPHERES 2 1.1.5 DEHN
SURGERY ON KNOTS 4 1.1.6 SURGERY ON LINKS 7 J.I.7 CONNECTED SUMS AND
SPLICING 9 1.1.8 SPLICE DECOMPOSITION 10 1.1.9 PLUMBING 12 1.1.10 LINKS
OF SINGULARITIES 16 1.1.11 MUTATIONS 18 1.1.12 BRANCHED COVERS 19 1.1.13
HEEGAARD SPLITTINGS OF HOMOLOGY SPHERES 25 1.2 RATIONAL HOMOLOGY SPHERES
26 1.2.1 SPHERICAL SPACE FORMS 26 1.2.2 DEHN SURGERY 29 1.2.3 SEIFERT
FIBERED MANIFOLDS 31 1.2.4 LINKS OF SINGULARITIES 32 1.2.5 BRANCHED
COVERS 33 2 ROKHLIN INVARIANT 35 2.1 THE ROKHLIN THEOREM 35 2.2
DEFINITION OF THE ROKHLIN INVARIANT 38 2.3 PROPERTIES OF THE ROKHLIN
INVARIANT 39 2.3.1 SURGERY FORMULA FOR THE ROKHLIN INVARIANT 39 2.3.2
SURGERY ON ALGEBRAICALLY SPLIT LINKS 41 2.3.3 SPLICING AND MUTATION 42
2.3.4 ROKHLIN INVARIANT OF BRANCHED COVERINGS 43 2.3.5 BIRMAN-CRAGGS
HOMOMORPHISMS 43 2.3.6 HOMOLOGY COBORDISM INVARIANCE 44 2.4 SEIFERT
FIBERED AND GRAPH HOMOLOGY SPHERES 45 2.4.1 THE ALGORITHM 45 2.4.2 THE
FORMULA 48 X TABLE OF CONTENTS 3 CASSON INVARIANT 51 3.1 DEFINITION OF
THE CASSON INVARIANT 51 3.2 CONSTRUCTION OF THE CASSON INVARIANT 54
3.2.1 5C/(2)-REPRESENTATION SPACES 54 3.2.2 THE INTERSECTION THEORY 55
3.2.3 ORIENTATIONS 57 3.2.4 INDEPENDENCE OF HEEGAARD SPLITTING 58 3.2.5
CASSON INVARIANT FOR KNOTS AND PROPERTY (1) 58 3.2.6 THE DIFFERENCE
CYCLE 60 3.2.7 CASSON INVARIANT FOR BOUNDARY LINKS AND PROPERTY (2) 61
3.2.8 CASSON INVARIANT OF A TREFOIL AND PROPERTY (0) 62 3.3 COMMENTS AND
RAMIFICATIONS 63 3.3.1 PILLOWCASE 63 3.3.2 PERTURBATIONS 66 3.3.3 THE
CONNECTED SUM FORMULA 67 3.3.4 THE INTEGRALITY OF X(E) 68 3.3.5 CASSON
INVARIANT OF ALGEBRAICALLY SPLIT LINKS 68 3.4 PROPERTIES OF THE CASSON
INVARIANT 69 3.4.1 SPLICING ADDITIVITY 69 3.4.2 MUTATION INVARIANCE 70
3.4.3 CASSON INVARIANT OF BRANCHED COVERINGS 70 3.4.4 CASSON INVARIANT
OF FIBERED KNOTS 73 3.4.5 FINITE TYPE INVARIANTS 73 3.4.6 FURTHER
PROPERTIES OF THE CASSON INVARIANT 74 3.5 SEIFERT FIBERED AND GRAPH
HOMOLOGY SPHERES 75 3.5.1 CASSON INVARIANT OF (P, Q,R) 75 3.5.2 CASSON
INVARIANT OF 27( A I»* * * A N) 78 3.5.3 THE NEUMANN-WAHL CONJECTURE
82 3.6 APPLICATIONS OF THE CASSON INVARIANT 83 3.6.1 TRIANGULATING
TOPOLOGICAL 4-MANIFOLDS 83 3.6.2 AMPHICHEIRAL HOMOLOGY SPHERES 84 3.6.3
PROPERTY P FOR KNOTS 85 4 INVARIANTS OF WALKER AND LESCOP 87 4.1
DEFINITION OF THE WALKER INVARIANT 87 4.2 CONSTRUCTION OF THE WALKER
INVARIANT 88 4.2.1 5C/(2)-REPRESENTATION VARIETIES 89 4.2.2 THE
INTERSECTION THEORY 89 4.2.3 THE SURGERY FORMULA 92 4.2.4 COMBINATORIAL
DEFINITION OF THE WALKER INVARIANT 92 4.3 THE LESCOP INVARIANT 93 4.4
PROPERTIES OF THE WALKER AND LESCOP INVARIANTS 95 4.4.1 THE GLUING
FORMULA 96 4.4.2 BRANCHED COVERS 96 4.4.3 SEIFERT FIBERED MANIFOLDS .
98 4.5 CASSON TYPE INVARIANTS FROM OTHER LIE GROUPS 98 TABLE OF CONTENTS
XI CASSON INVARIANT AND GAUGE THEORY 99 5.1 GAUGE THEORY IN DIMENSION 3
99 5.2 CHERN-SIMONS FUNCTION 101 5.3 THE CASSON INVARIANT FROM GAUGE
THEORY 103 5.3.1 MORSE THEORY AND EULER CHARACTERISTIC 103 5.3.2
CRITICAL POINTS OF CS AND SPECTRAL FLOW 103 5.3.3 NON-DEGENERATE CASE
105 5.3.4 PERTURBATIONS 106 5.3.5 MORSE-TYPE PERTURBATIONS 108 5.3.6
CASSON INVARIANT AND SEIBERG-WITTEN EQUATIONS 109 5.4 CASSON-TYPE
INVARIANTS OF KNOTS 110 5.4.1 REPRESENTATION VARIETIES OF KNOT GROUPS
110 5.4.2 THE INVARIANTS 112 5.5 EQUIVARIANT CASSON INVARIANT 113 5.5.1
EQUIVARIANT GAUGE THEORY 113 5.5.2 DEFINITION OF THE INVARIANTS 114
5.5.3 EQUIVARIANT CASSON AND KNOT SIGNATURES 115 5.5.4 APPLICATIONS 116
5.6 .THE SU(Z) CASSON INVARIANT 118 5.6.1 SOME ST/(3)-GAUGE THEORY 119
5.6.2 DEFINITION OF THE INVARIANT 119 5.6.3 PROPERTIES AND COMPUTATIONS
121 INSTANTON FLOER HOMOLOGY 123 6.1 GAUGE THEORY IN DIMENSION 4 123
6.1.1 GAUGE THEORY ON CLOSED 4-MANIFOLDS 123 6.1.2 GAUGE THEORY ON OPEN
4-MANIFOLDS 125 6.1.3 LINEAR ANALYSIS 126 6.1.4 NON-LINEAR ANALYSIS 129
6.2 DEFINITION OF THE FLOER HOMOLOGY 130 6.2.1 REVIEW OF THE MORSE
THEORY 131 6.2.2 FLOER HOMOLOGY OF INTEGRAL HOMOLOGY SPHERES 131 6.2.3
FUNCTORIALITY WITH RESPECT TO COBORDISMS 135 6.3 SPECTRAL FLOW FORMULAS
137 6.3.1 THE ATIYAH-PATODI-SINGER FORMULA 137 6.3.2 THE SPLITTING
FORMULA 139 6.3.3 THE KIRK-KLASSEN FORMULA 141 6.4 SEIFERT FIBERED AND
GRAPH HOMOLOGY SPHERES 143 6.4.1 THE ALGORITHM 143 6.4.2 THE CLOSED FORM
FORMULA 146 6.4.3 GRAPH HOMOLOGY SPHERES 148 6.5 PROPERTIES OF THE FLOER
HOMOLOGY 149 6.5.1 ORIENTATION REVERSAL 150 6.5.2 FLOER HOMOLOGY OF
HOMOLOGY HANDLES 150 6.5.3 THE FLOER EXACT TRIANGLE 152 XII TABLE OF
CONTENTS 6.5.4 SPECIAL BOUNDARY MAPS 159 6.5.5 THE U-MAP IN FLOER
HOMOLOGY 159 6.5.6 INTEGER GRADED FLOER HOMOLOGY 161 6.5.7 FLOER
HOMOLOGY OF CONNECTED SUMS 163 6.5.8 FUNCTORIALITY WITH RESPECT TO
DIFFEOMORPHISMS 166 6.5.9 MUTATION INVARIANCE 167 6.6 FLOER HOMOLOGY IN
DONALDSON THEORY 167 6.6.1 DONALDSON INVARIANTS OF CLOSED 4-MANIFOLDS
167 6.6.2 RELATIVE DONALDSON POLYNOMIALS 171 6.6.3 THE GLUING FORMULA
175 6.7 EXTENDING FLOER HOMOLOGY 177 6.7.1 EQUIVARIANT FLOER HOMOLOGY
177 6.7.2 FUKAYA-FLOER HOMOLOGY 179 6.7.3 FLOER S CATEGORY AND FUNCTOR
179 6.7.4 THE ATIYAH-FLOER CONJECTURE 181 6.7.5 FLOER HOMOLOGY OF KNOTS
181 6.7.6 SEIBERG-WITTEN FLOER HOMOLOGY 183 7 THE HOMOLOGY COBORDISM
GROUP 185 7.1 HOMOLOGY COBORDISMS 185 7.1.1 MAZUR HOMOLOGY SPHERES 185
7.1.2 KNOT COBORDISMS AND HOMOLOGY COBORDISMS 187 7.1.3 RIBBON
CONCORDANCES AND RIBBON KNOTS 189 7.1.4 BRANCHED COVERINGS 190 7.2 THE
STRUCTURE OF 9F 190 7.2.1 A CLASSICAL APPROACH TO 9| 191 7.2.2
INFINITE ORDER ELEMENTS IN 9| 191 7.2.3 THE /2-INVARIANT 196 7.2.4 THE
FUKUMOTO-FURUTA INVARIANTS 197 7.2.5 THE GROUP 6 | IS INFINITELY
GENERATED 199 7.3 APPLICATIONS OF THE HOMOLOGY COBORDISM GROUP 200 7.3.1
TRIANGULATING TOPOLOGICAL MANIFOLDS 200 7.3.2 KNOT CONCORDANCE GROUP 200
7.3.3 PL-DISCS IN CONTRACTIBLE 4-MANIFOLDS 201 7.3.4 CONSTRUCTING SMOOTH
MANIFOLDS 202 REFERENCES 205 INDEX 219
|
| any_adam_object | 1 |
| author | Saveliev, Nikolai 1966- |
| author_GND | (DE-588)121274896 |
| author_facet | Saveliev, Nikolai 1966- |
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| building | Verbundindex |
| bvnumber | BV014603470 |
| classification_rvk | SK 300 SK 350 |
| ctrlnum | (OCoLC)440686105 (DE-599)BVBBV014603470 |
| discipline | Mathematik |
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| id | DE-604.BV014603470 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:13Z |
| institution | BVB |
| isbn | 3540437967 9783642078491 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009926724 |
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| physical | XII, 223 S. graph. Darst. |
| publishDate | 2002 |
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| publishDateSort | 2002 |
| publisher | Springer |
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| series | Encyclopaedia of mathematical sciences |
| series2 | Encyclopaedia of mathematical sciences Encyclopaedia of mathematical sciences / Low-dimensional topology |
| spelling | Saveliev, Nikolai 1966- Verfasser (DE-588)121274896 aut Invariants for homology 3-spheres Nikolai Saveliev Berlin [u.a.] Springer 2002 XII, 223 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopaedia of mathematical sciences 140 Encyclopaedia of mathematical sciences / Low-dimensional topology 1 Hier auch später erschienene, unveränderte Nachdrucke Invariante (DE-588)4128781-2 gnd rswk-swf Niederdimensionale Topologie (DE-588)4280826-1 gnd rswk-swf Homologiesphäre (DE-588)4284581-6 gnd rswk-swf Niederdimensionale Topologie (DE-588)4280826-1 s DE-604 Homologiesphäre (DE-588)4284581-6 s Invariante (DE-588)4128781-2 s Low-dimensional topology Encyclopaedia of mathematical sciences 1 (DE-604)BV014813608 1 Encyclopaedia of mathematical sciences 140 (DE-604)BV024126459 140 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009926724&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Saveliev, Nikolai 1966- Invariants for homology 3-spheres Encyclopaedia of mathematical sciences Invariante (DE-588)4128781-2 gnd Niederdimensionale Topologie (DE-588)4280826-1 gnd Homologiesphäre (DE-588)4284581-6 gnd |
| subject_GND | (DE-588)4128781-2 (DE-588)4280826-1 (DE-588)4284581-6 |
| title | Invariants for homology 3-spheres |
| title_auth | Invariants for homology 3-spheres |
| title_exact_search | Invariants for homology 3-spheres |
| title_full | Invariants for homology 3-spheres Nikolai Saveliev |
| title_fullStr | Invariants for homology 3-spheres Nikolai Saveliev |
| title_full_unstemmed | Invariants for homology 3-spheres Nikolai Saveliev |
| title_short | Invariants for homology 3-spheres |
| title_sort | invariants for homology 3 spheres |
| topic | Invariante (DE-588)4128781-2 gnd Niederdimensionale Topologie (DE-588)4280826-1 gnd Homologiesphäre (DE-588)4284581-6 gnd |
| topic_facet | Invariante Niederdimensionale Topologie Homologiesphäre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009926724&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014813608 (DE-604)BV024126459 |
| work_keys_str_mv | AT savelievnikolai invariantsforhomology3spheres |