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• W3136195633 abstract "Abstract We prove that every spherical object in the derived Fukaya category of a closed surface of genus at least $2$ whose Chern character represents a nonzero Hochschild homology class is quasi-isomorphic to a simple closed curve equipped with a rank $1$ local system. (The homological hypothesis is necessary.) This largely answers a question of Haiden, Katzarkov and Kontsevich. It follows that there is a natural surjection from the autoequivalence group of the Fukaya category to the mapping class group. The proofs appeal to and illustrate numerous recent developments: quiver algebra models for wrapped categories, sheafifying the Fukaya category, equivariant Floer theory for finite and continuous group actions and homological mirror symmetry. An application to high-dimensional symplectic mapping class groups is included." @default.
• W3136195633 created "2021-03-29" @default.
• W3136195633 creator A5037530440 @default.
• W3136195633 creator A5038533970 @default.
• W3136195633 date "2021-01-01" @default.
• W3136195633 modified "2023-09-26" @default.
• W3136195633 title "Fukaya categories of surfaces, spherical objects and mapping class groups" @default.
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• W3136195633 doi "https://doi.org/10.1017/fms.2021.21" @default.
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