Fukaya categories of higher-genus surfaces and pants decompositions

In this paper we prove a local-to-global principle for the Fukaya category of a closed Riemann surface $\mathrm{\Sigma }$ of genus $g\ge 2$. We show that $\mathrm{F}\mathrm{u}\mathrm{k}(\mathrm{\Sigma })$ can be glued from the Fukaya categories of the pairs-of-pants making up a pants decomposition of $\mathrm{\Sigma }$. 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 $\mathrm{F}\mathrm{u}\mathrm{k}(\mathrm{\Sigma })$.