Haniya Azam, Christian Blanchet
Published 2019-03-28Version 1
We construct the Fukaya category of a surface with genus greater than one and compute its Grothendieck group. We consider here a topological variant, in which we disregard the area form and use instead an admissibility condition borrowed from Heegaard-Floer theory which ensures invariance under isotopy. We also study action of the mapping class group of the surface on its Fukaya category and establish faithfulness.
Fukaya categories and bordered Heegaard-Floer homology
On dynamics of the Mapping class group action on relative $\text{PSL}(2,\mathbb{R})$-Character Varieties
On the mapping class group action on the homology of surface covers
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