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Topological Fukaya category and mirror symmetry for punctured surfaces
- Part of
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- Journal:
- Compositio Mathematica / Volume 155 / Issue 3 / March 2019
- Published online by Cambridge University Press:
- 14 March 2019, pp. 599-644
- Print publication:
- March 2019
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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
$\unicode[STIX]{x1D6F4}$ via the topological Fukaya category. We prove that the topological Fukaya category of 
$\unicode[STIX]{x1D6F4}$ 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.
