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arXiv · 2103.03366

Fukaya categories of higher-genus surfaces and pants decompositions

James Pascaleff·Nicolò Sibilla
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Abstract

In this paper we prove a local-to-global principle for the Fukaya category of a closed Riemann surface $\Sigma$ of genus $g \geq 2$. We show that $\mathrm{Fuk}(\Sigma)$ can be glued from the Fukaya categories of the pairs-of-pants making up a pants decomposition of $\Sigma$. This extends our earlier results for the case of punctured Riemann surfaces. Our result has several interesting consequences: we obtain simple proofs of old and new HMS statements for Riemann surfaces, and establish a geometrization theorem for the objects of $\mathrm{Fuk}(\Sigma)$.

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James Pascaleff, Nicolò Sibilla. 2021-03-04. Fukaya categories of higher-genus surfaces and pants decompositions. https://arxiv.org/abs/2103.03366

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