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Bordered Heegaard Floer homology

Author: R Lipshitz; Peter Steven Ozsváth; Dylan P Thurston; American Mathematical Society,
Publisher: Providence, RI : American Mathematical Society, [2018] ©2018
Series: Memoirs of the American Mathematical Society, no. 1216.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Lipshitz, R. (Robert),
Bordered Heegaard Floer homology
(DLC) 2018029366
(OCoLC)1031562142
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: R Lipshitz; Peter Steven Ozsváth; Dylan P Thurston; American Mathematical Society,
ISBN: 1470447487 9781470447489
OCLC Number: 1042567293
Notes: "July 2018, volume 254, number 1216 (fourth of 5 numbers)"
Keywords: Three-manifold topology, low-dimensional topology, Heegaard Floer homology, holomorphic curves, extended topological field theory.
Description: 1 online resource (viii, 279 pages) : illustrations.
Contents: 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 5.3. Holomorphic curves in \textalt{\RR× ×[0,1]×\RR} R × Z × [0,1] × R5.4. 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 diagramsChapter 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
Series Title: Memoirs of the American Mathematical Society, no. 1216.
Responsibility: Robert Lipshitz, Peter S. Ozsvath, Dylan P. Thurston.

Abstract:

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  Read more...

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