Fukaya A∞-structures associated to Lefschetz fibrations. I

By P. Seidel. 2009

51 citations recorded by the source corpus.

This (partially expository) paper discusses Lagrangian Floer cohomology in the context of Lefschetz fibrations, with emphasis on the algebraic structures encountered there. In addition to the well-known directed A_infinity algebras which appear in this situation, one has additional information encoded in a certain bimodule homomorphism. There are two approaches to constructing this homomorphism: in terms of the (noncompact) Lefschetz thimbles in the total space, or else in terms of vanishing cycle in the fibre. We prove a comparison result, which shows that (up to a certain remaining ambiguity) the two approaches are equivalent.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/345c7ef5a4066ee9f724d7769d0aec7215c108cf

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces (2012, methodology): “These technical problems were resolved by Seidel in [41], by introducing a method of defining Fukaya categories of Lefschetz fibration that generalizes in a straightforward way to the Morse-Bott case we are considering.”
Khovanov homology from Floer cohomology (2015, methodology): “We shall adopt a viewpoint which is a mixture of Seidel’s approach in [47] and Abouzaid-Seidel’s approach in [5], and where the Lagrangians we consider are similar to those studied by Biran and Cornea in [11, 12].”