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arXiv · 1604.06448

Topological Fukaya category and mirror symmetry for punctured surfaces

James Pascaleff·Nicolò Sibilla
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Abstract

In this paper we establish a version of homological mirror symmetry for punctured Riemann surfaces. Following a proposal of Kontsevich we model A-branes on a punctured surface $\Sigma$ via the topological Fukaya category. We prove that the topological Fukaya category of $\Sigma$ is equivalent to the category of matrix factorizations of the mirror LG model $(X,W)$. Along the way we establish new gluing results for the topological Fukaya category of punctured surfaces which might be of independent interest.

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James Pascaleff, Nicolò Sibilla. 2016-04-21. Topological Fukaya category and mirror symmetry for punctured surfaces. https://doi.org/10.1112/s0010437x19007073

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