Topological Fukaya categories of surfaces

Abstract

We construct the topological Fukaya category of a surface with genus greater than one, making this model intrinsic to the topology of the surface. Instead of using the area form of the surface, we use an admissibility condition borrowed from Heegaard-Floer theory which ensures invariance under isotopy . In this paper we show finiteness of the moduli space using purely topological means and compute the Grothendieck group of the topological Fukaya category. We also show the faithfulness of MCG-action on the topological Fukaya category in this setup.