Fukaya categories of symmetric products and bordered Heegaard-Floer homology

By D. Auroux. 2010

81 citations recorded by the source corpus.

The main goal of this paper is to discuss a symplectic interpretation of Lipshitz, Ozsvath and Thurston's bordered Heegaard-Floer homology in terms of Fukaya categories of symmetric products and Lagrangian correspondences. More specifically, we give a description of the algebra A(F) which appears in the work of Lipshitz, Ozsvath and Thurston in terms of (partially wrapped) Floer homology for product Lagrangians in the symmetric product, and outline how bordered Heegaard-Floer homology itself can conjecturally be understood in this language.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5605bd8194087848579d28c8c96a0aa795f110f2

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Lagrangian cobordism. I (2011, background): “instance the works of Seidel [Sei3], Abouzaid [Abo], Auroux [Aur], as well as older work of Oh [Oh4]).”
Auslander orders over nodal stacky curves and partially wrapped Fukaya categories (2017, background): “E i,j : Si,j [3] → P i,j [2] → P i,j+1[1] (3.”
Fukaya categories and bordered Heegaard-Floer homology (2010, background): “8 essentially follows from the fact that the A∞-functors induced by the correspondences Tα and (−Tα) on one hand, and Tβ and (−Tβ) on the other hand, are adjoint to each other; see Proposition 6.6 in [2] for the case of A∞-modules. The case where one of k± vanishes, say k− = 0, is of particular inte”
Bordered Floer homology for manifolds with torus boundary via immersed curves (2016, background): “Following the introduction of bordered Floer homology [24, 25], Auroux [2, 3] and Lekili and Perutz [22] suggested that the Floer homology of a compact oriented M with ∂M = Σg should be an object in F(Symg(Σg \ z)).”
Heegaard Floer homology as morphism spaces (2010, methodology): “In particular, Auroux’s paper [1] led us to a dramatically simplified argument.”
A Beginner’s Introduction to Fukaya Categories (2013, background): “[13, 14] The Lagrangian submanifolds Ds = ∏ i∈s αi, s ⊆ {1, .”