Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fukaya categories of surfaces, spherical objects, and mapping class
  groups   We prove that every spherical object in the derived Fukaya category of a
closed surface of genus at least two whose Chern character represents a
non-zero Hochschild homology class is quasi-isomorphic to a simple closed curve
equipped with a rank one 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.

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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th