Bordered Heegaard Floer homology

By Robert Lipshitz, Peter S. Ozsv'ath, Dylan Thurston. Memoirs of the American Mathematical Society, 2008

155 citations recorded by the source corpus.

We 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 A-infinity module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A-infinity tensor product of the type D module of one piece and the type A module from the other piece is HF^ of the glued manifold. As a special case of the construction, we 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 HF^. We relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/48476cf542263002cc979ba0dffb3ad7e7dbf601

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Liam Watson
2. A. Levine
3. M. Hedden
4. Jacob Rasmussen
5. Jennifer Hom
6. David Krcatovich
7. Yi Ni
8. E. Gorsky

In Mathematical Physics

1. Liam Watson
2. A. Levine
3. M. Hedden
4. Jacob Rasmussen
5. Jennifer Hom
6. David Krcatovich
7. Yi Ni
8. E. Gorsky

In Neurology

1. Liam Watson
2. M. Hedden
3. A. Levine
4. Jennifer Hom
5. Jacob Rasmussen
6. E. Gorsky
7. Ina Petkova

Citations in the corpus

• NONSURJECTIVE SATELLITE OPERATORS AND PIECEWISE-LINEAR CONCORDANCE (2014, methodology): “trengthens both of these results. (See Remark 4.1 for more details.) We assume throughout the paper that the reader is familiar with both knot Floer homology [21] and bordered Heegaard Floer homology [16, 17]; for a quick summary of the latter, see the author’s exposition in [15, Section 2]. All Flo”
• On the geography and botany of knot Floer homology (2014, methodology): “he Tor terms which naturally arise in the context of F[U]-modules. ON THE GEOGRAPHY AND BOTANY OF KNOT FLOER HOMOLOGY 13 Floer homology is also well-understood under more general satellite operations [26, 27, 28, 36, 47, 76, 78]. We discuss these results (and their implications for this work) furthe”
• Floer simple manifolds and L-space intervals (2015, unknown): “Following Chapter 11 of [29], we can think of the module structure as being specified by a pair of vector spaces V , V 1 over the field of two elements F2, together with linear maps D1, D3, D123 : V 0 → V 1 D2 : V 1 → V 0 D12 : V 0 → V 0 D23 : V 1 → V 1 where ĈFD(Y, μ, λ) = A(Z) ⊗F2 (V 0 ⊕ V (1)) an”