Noncompact description for Fukaya-Seidel categories of invertible curve singularities

Abstract: For given invertible polynomial W, we consider two types of Fukaya category. One is the usual Fukaya-Seidel category from Lefschetz fibration structure of W. For the maximal symmetry group G of W, we can construct the other Fukaya category of the pair (W,G) from wrapped Fukaya category of the Milnor fiber and quantum cap action of monodromy orbit. In this talk, we compare the equivariant lift of the latter with the Fukaya-Seidel category and prove its derived equivalence for invertible curve singularities. In particular, directedness of the category is obtained from quantum cap action and related constructions. This talk is based on the joint work (in progress) with Cheol-hyun Cho (SNU) and Dongwook Choa (KIAS).

mathematical physicsalgebraic geometrysymplectic geometry

Audience: researchers in the topic

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