Fukaya category of surfaces and mapping class group action

2019/03/28 by Haniya Azam, Azam, Haniya, Christian Blanchet +1
Mathematics · #53D37 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1903.11928

openalex publication_date 2019/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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