Fukaya categories and bordered Heegaard-Floer homology

By D. Auroux. 2010

46 citations recorded by the source corpus.

We outline an interpretation of Heegaard-Floer homology of 3-manifolds (closed or with boundary) in terms of the symplectic topology of symmetric products of Riemann surfaces, as suggested by recent work of Tim Perutz and Yanki Lekili. In particular we discuss the connection between the Fukaya category of the symmetric product and the bordered algebra introduced by Robert Lipshitz, Peter Ozsvath and Dylan Thurston, and recast bordered Heegaard-Floer homology in this language.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a938b3b66c9477c3c4ecf574c05b45b2930bd10c

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Citations in the corpus

Flat surfaces and stability structures (2014, unknown): “We also thank Mohammed Abouzaid, Denis Auroux, Tom Bridgeland, Igor Burban, Tobias Dyckerhoff, Alexander Efimov, Alexander Goncharov, Dominic Joyce, Mikhail Kapranov, Gabriel Kerr, Andrew Neitzke, Tony Pantev, Yan Soibelman, Pawel Sosna, and Zachary Sylvan for discussions relating to this paper.”
Fukaya categories of symmetric products and bordered Heegaard-Floer homology (2010, background): “Thus, it should be viewed not as a new result, but rather as a different insight into the main result in [8] (see also [3] and [9] for recent developments).”
Microlocal Morse theory of wrapped Fukaya categories (2018, background): “The framework of partially wrapped Fukaya categories [14, 15, 83, 34, 35] has emerged as a way to describe and relate different prescriptions for asymptotics and wrapping.”
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)).”
A Beginner’s Introduction to Fukaya Categories (2013, unknown): “[13, 14] The Lagrangian submanifolds Ds = ∏ i∈s αi, s ⊆ {1, .”
Sectorial descent for wrapped Fukaya categories (2018, methodology): “Let us begin by fixing our notation and terminology for partially wrapped Fukaya categories (see §2 for a full treatment); our setup is rather more general than that considered before [7, 8, 42, 32, 26].”