Bordered Heegaard Floer Homology. (Record no. 4679)
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| 000 -LEADER | |
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| fixed length control field | 05992nam a22005173i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC5501883 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724113326.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2018 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470447489 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470428884 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC5501883 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL5501883 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1042567293 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA665 .L577 2018 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.3/6 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Lipshitz, Robert. |
| 245 10 - TITLE STATEMENT | |
| Title | Bordered Heegaard Floer Homology. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2018. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2018. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (294 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.254 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 1. Introduction -- 1.1. Background -- 1.2. The bordered Floer homology package -- 1.3. On gradings -- 1.4. The case of three-manifolds with torus boundary -- 1.5. Previous work -- 1.6. Further developments -- 1.7. Organization -- Acknowledgments -- Chapter 2. \textalt{\Ainf}A-infty structures -- 2.1. \textalt{\Ainf}A-infty algebras and modules -- 2.2. \textalt{\Ainf}A-infty tensor products -- 2.3. Type \textalt{ }D structures -- 2.4. Another model for the \textalt{\Ainf}A-infty tensor product -- 2.5. Gradings by non-commutative groups -- Chapter 3. The algebra associated to a pointed matched circle -- 3.1. The strands algebra \textalt{\Alg( , )}A(n,k) -- 3.2. Matched circles and their algebras -- 3.3. Gradings -- Chapter 4. Bordered Heegaard diagrams -- 4.1. Bordered Heegaard diagrams: definition, existence, and uniqueness -- 4.2. Examples of bordered Heegaard diagrams -- 4.3. Generators, homology classes and \textalt{\spin^{ }}spin-c structures -- 4.4. Admissibility criteria -- 4.5. Closed diagrams -- Chapter 5. Moduli spaces -- 5.1. Overview of the moduli spaces -- 5.2. Holomorphic curves in \textalt{Σ×[0,1]×\RR}Sigma × [0,1] × R -- 5.3. Holomorphic curves in \textalt{\RR× ×[0,1]×\RR} R × Z × [0,1] × R -- 5.4. Compactifications via holomorphic combs -- 5.5. Gluing results for holomorphic combs -- 5.6. Degenerations of holomorphic curves -- 5.7. More on expected dimensions -- Chapter 6. Type \textalt{ }D modules -- 6.1. Definition of the type \textalt{ }D module -- 6.2. \textalt{\bdy²=0}Boundary-squared is zero -- 6.3. Invariance -- 6.4. Twisted coefficients -- Chapter 7. Type \textalt{ }A modules -- 7.1. Definition of the type \textalt{ }A module -- 7.2. Compatibility with algebra -- 7.3. Invariance -- 7.4. Twisted coefficients -- Chapter 8. Pairing theorem via nice diagrams. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Chapter 9. Pairing theorem via time dilation -- 9.1. Moduli of matched pairs -- 9.2. Dilating time -- 9.3. Dilating to infinity -- 9.4. Completion of the proof of the pairing theorem -- 9.5. A twisted pairing theorem -- 9.6. An example -- Chapter 10. Gradings -- 10.1. Algebra review -- 10.2. Domains -- 10.3. Type \textalt{ }A structures -- 10.4. Type \textalt{ }D structures -- 10.5. Refined gradings -- 10.6. Tensor product -- Chapter 11. Bordered manifolds with torus boundary -- 11.1. Torus algebra -- 11.2. Surgery exact triangle -- 11.3. Preliminaries on knot Floer homology -- 11.4. From \textalt{\CFDa}CFDˆ to \textalt{\HFKm}HFK- -- 11.5. From \textalt{\CFKm}CFK- to \textalt{\CFDa}CFDˆ: Statement of results -- 11.6. Generalized coefficient maps and boundary degenerations -- 11.7. From \textalt{\CFKm}CFK- to \textalt{\CFDa}CFDˆ: Basis-free version -- 11.8. Proof of Theorem 11.26 -- 11.9. Satellites revisited -- Appendix A. Bimodules and change of framing -- A.1. Statement of results -- A.2. Sketch of the construction -- A.3. Computations for \textalt{3}3-manifolds with torus boundary -- A.4. From \textalt{\HFK}HFK to \textalt{\CFDa}CFDˆ for arbitrary integral framings -- Bibliography -- Index of Definitions -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an \mathcal A_\infty module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the \mathcal A_\infty tensor product of the type D module of one piece and the type A module from the other piece is \widehat{HF} of the glued manifold. As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for \widehat{HF}. The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Floer homology. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Three-manifolds (Topology). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Topological manifolds. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Symplectic geometry. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Ozsváth, Peter. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Thurston, Dylan P. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Lipshitz, Robert |
| Title | Bordered Heegaard Floer Homology |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2018 |
| International Standard Book Number | 9781470428884 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5501883">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5501883</a> |
| Public note | Click to View |
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