Bordered Heegaard Floer homology:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
July 2018
|
| Series: | Memoirs of the American Mathematical Society
volume 254, number 1216 (fourth of 5 numbers) |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | viii, 279, 4 ungezählte Seiten Illustrationen |
| ISBN: | 9781470428884 |
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MARC
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| 245 | 1 | 0 | |a Bordered Heegaard Floer homology |c Robert Lipshitz, Peter S. Ozsváth, Dylan P. Thurston |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c July 2018 | |
| 264 | 4 | |c © 2018 | |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 254, number 1216 (fourth of 5 numbers) | |
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| 700 | 1 | |a Thurston, Dylan P. |4 aut | |
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Record in the Search Index
| _version_ | 1804178872808243200 |
|---|---|
| adam_text | Contents
Chapter 1. Introduction..................................................... 1
1.1. Background......................................................... 1
1.2. The bordered Floer homology package................................. 3
1.3. On gradings ........................................................ 5
1.4. The case of three-manifolds with torus boundary..................... 6
1.5. Previous work ...................................................... 6
1.6. Further developments ............................................... 7
1.7. Organization ....................................................... 7
Acknowledgments....................................................... 8
Chapter 2. Moo structures................................................. 9
2.1. Aoo algebras and modules............................................ 9
2.2. Aoo tensor products ............................................... 15
2.3. Type D structures.................................................. 17
2.4. Another model for the Aoo tensor product .......................... 22
2.5. Gradings by non-commutative groups ................................ 26
Chapter 3. The algebra associated to a pointed matched circle ............. 29
3.1. The strands algebra A(n, k)........................................ 29
3.2. Matched circles and their algebras ................................ 34
3.3. Gradings .......................................................... 38
Chapter 4. Bordered Heegaard diagrams ..................................... 45
4.1. Bordered Heegaard diagrams: definition, existence, and uniqueness . 45
4.2. Examples of bordered Heegaard diagrams............................. 51
4.3. Generators, homology classes and spinc structures ................. 53
4.4. Admissibility criteria ............................................ 56
4.5. Closed diagrams ................................................... 58
Chapter 5. Moduli spaces................................................... 61
5.1. Overview of the moduli spaces ..................................... 61
5.2. Holomorphic curves in E x [0,1] x M................................ 64
5.3. Holomorphic curves in R x Z x [0,1] x R ........................... 70
5.4. Compactifications via holomorphic combs............................ 73
5.5. Gluing results for holomorphic combs .............................. 82
5.6. Degenerations of holomorphic curves................................ 89
5.7. More on expected dimensions........................................ 99
Chapter 6. Type D modules ................................. ............109
iii
IV
CONTENTS
6.1. Definition of the type D module ..................................109
6.2. d2 = 0..............................................................111
6.3. Invariance ..........................................................HO
6.4. Twisted coefficients ...............................................142
Chapter 7. Type A modules ...................................................145
7.1. Definition of the type A module ....................................145
7.2. Compatibility with algebra .........................................147
7.3. Invariance .........................................................150
7.4. Twisted coefficients ...............................................155
Chapter 8. Pairing theorem via nice diagrams ................................157
Chapter 9. Pairing theorem via time dilation ................................161
9.1. Moduli of matched pairs ............................................162
9.2. Dilating time.......................................................165
9.3. Dilating to infinity................................................171
9.4. Completion of the proof of the pairing theorem......................183
9.5. A twisted pairing theorem ..........................................184
9.6. An example......................................................... 185
Chapter 10. Gradings ........................................................189
10.1. Algebra review .....................................................189
10.2. Domains.............................................................190
10.3. Type A structures ..................................................193
10.4. Type D structures ..................................................197
10.5. Refined gradings ...................................................199
10.6. Tensor product .....................................................201
Chapter 11. Bordered manifolds with torus boundary ........................205
11.1. Torus algebra.......................................................205
11.2. Surgery exact triangle ........................................208
11.3. Preliminaries on knot Floer homology ...............................209
11.4. From CFD to HFK^....................................................212
11.5. From CFK~ to CFD: Statement of results ..................216
11.6. Generalized coefficient maps and boundary degenerations ............220
11.7. From CFK~ to CFD: Basis-free version....................225
11.8. Proof of Theorem 11.26 244
11.9. Satellites revisited ...............................................250
Appendix A. Bimodules and change of framing.............................255
A.l. Statement of results.................................................255
A.2. Sketch of the construction ........................................ 256
A.3. Computations for 3-manifolds with torus boundary ....................261
A.4. From HFK to CFD for arbitrary integral framings .....................265
Bibliography.................................................................269
Index of Definitions ........................................................273
|
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| author | Lipshitz, Robert Ozsváth, Peter Steven 1967- Thurston, Dylan P. |
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| indexdate | 2024-07-10T08:10:53Z |
| institution | BVB |
| isbn | 9781470428884 |
| language | English |
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| physical | viii, 279, 4 ungezählte Seiten Illustrationen |
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| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Lipshitz, Robert (DE-588)1124952543 aut Bordered Heegaard Floer homology Robert Lipshitz, Peter S. Ozsváth, Dylan P. Thurston Providence, Rhode Island American Mathematical Society July 2018 © 2018 viii, 279, 4 ungezählte Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 254, number 1216 (fourth of 5 numbers) Ozsváth, Peter Steven 1967- (DE-588)1081461268 aut Thurston, Dylan P. aut Memoirs of the American Mathematical Society volume 254, number 1216 (fourth of 5 numbers) (DE-604)BV008000141 1216 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030569777&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lipshitz, Robert Ozsváth, Peter Steven 1967- Thurston, Dylan P. Bordered Heegaard Floer homology Memoirs of the American Mathematical Society |
| title | Bordered Heegaard Floer homology |
| title_auth | Bordered Heegaard Floer homology |
| title_exact_search | Bordered Heegaard Floer homology |
| title_full | Bordered Heegaard Floer homology Robert Lipshitz, Peter S. Ozsváth, Dylan P. Thurston |
| title_fullStr | Bordered Heegaard Floer homology Robert Lipshitz, Peter S. Ozsváth, Dylan P. Thurston |
| title_full_unstemmed | Bordered Heegaard Floer homology Robert Lipshitz, Peter S. Ozsváth, Dylan P. Thurston |
| title_short | Bordered Heegaard Floer homology |
| title_sort | bordered heegaard floer homology |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030569777&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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