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 Σ via the topological Fukaya category. We prove that the topological Fukaya category of σ is equivalent to the category of matrix factorizations of a certain mirror LG model (X,W). Along the way we establish new gluing results for the topological Fukaya category of punctured surfaces which are of independent interest.

Topological Fukaya category and mirror symmetry for punctured surfaces / Pascaleff, J.; Sibilla, N.. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - 155:3(2019), pp. 599-644. [10.1112/S0010437X19007073]

Topological Fukaya category and mirror symmetry for punctured surfaces

Sibilla N.
2019-01-01

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 Σ via the topological Fukaya category. We prove that the topological Fukaya category of σ is equivalent to the category of matrix factorizations of a certain mirror LG model (X,W). Along the way we establish new gluing results for the topological Fukaya category of punctured surfaces which are of independent interest.
2019
155
3
599
644
Pascaleff, J.; Sibilla, N.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/117697
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