Mirror symmetry and Fukaya categories of singular hypersurfaces
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DOI: 10.1016/j.aim.2021.108116
Abstract: We consider a definition of the Fukaya category of a singular hypersurface proposed by Auroux, given by localizing the Fukaya category of a nearby fiber at Seidel's natural transformation, and show that this possesses several… read more here.
Keywords: category; fukaya categories; fukaya; symmetry fukaya ... See more keywords
Fukaya categories of surfaces, spherical objects and mapping class groups
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DOI: 10.1017/fms.2021.21
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… read more here.
Keywords: class; fukaya categories; fukaya category; categories surfaces ... See more keywords
Calabi–Yau structures on topological Fukaya categories
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DOI: 10.1112/s0010437x25007109
Abstract: Abstract We develop a local-to-global formalism for constructing Calabi–Yau structures for global sections of constructible sheaves or cosheaves of differential graded categories. The required data (a morphism between the sheafified Hochschild homology with the topological… read more here.
Keywords: structures topological; fukaya categories; yau structures; calabi yau ... See more keywords