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2014 | OriginalPaper | Chapter

Notes on Bordered Floer Homology

Authors : Robert Lipshitz, Peter Ozsváth, Dylan P. Thurston

Published in: Contact and Symplectic Topology

Publisher: Springer International Publishing

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Abstract

Bordered Heegaard Floer homology is an extension of Ozsváth-Szabós Heegaard Floer homology to 3-manifolds with boundary, enjoying good properties with respect to gluings. In these notes we will introduce the key features of bordered Heegaard Floer homology: its formal structure, a precise definition of the invariants of surfaces, a sketch of the definitions of the 3-manifold invariants, and some hints at the analysis underlying the theory. We also talk about bordered Heegaard Floer homology as a computational tool, both in theory and practice.

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previous chapter Contact Invariants in Floer Homology

next chapter Stein Structures: Existence and Flexibility

Strictly speaking, in the original definition the manifolds were only totally-real, not Lagrangian. It was shown in [54] that a Kähler form can be chosen making the relevant submanifolds Lagrangian.

The ground ring for bordered Floer homology is \(\mathbb {Z}/{2}\mathbb {Z}\); hence the signs usually appearing in the differential graded Leibniz rule become irrelevant.

This I(S) was denoted I _D(S) in [27], where I(S) was used for I _A(S) introduced in Section 4.4.

The discussion in this section is taken from [27, Section 11.2].

As usual, we will suppress the fact that one needs to perturb the almost-complex structure in order to achieve transversality from the discussion.

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Title: Notes on Bordered Floer Homology
Authors: Robert Lipshitz
Peter Ozsváth
Dylan P. Thurston
Publisher: Springer International Publishing
Book: Contact and Symplectic Topology
Print ISBN: 978-3-319-02035-8

Electronic ISBN: 978-3-319-02036-5

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-3-319-02036-5_7

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