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• W2105600529 startingPage "1473" @default.
• W2105600529 abstract "For a triangulated category A with a 2-periodic dg-enhancement and a triangulated oriented marked surface S we introduce a dg-category F(S,A) parametrizing systems of exact triangles in A labelled by triangles of S. Our main result is that F(S,A) is independent on the choice of a triangulation of S up to essentially unique Morita equivalence. In particular, it admits a canonical action of the mapping class group. The proof is based on general properties of cyclic 2-Segal spaces. In the simplest case, where A is the category of 2-periodic complexes of vector spaces, F(S,A) turns out to be a purely topological model for the Fukaya category of the surface S. Therefore, our construction can be seen as implementing a 2-dimensional instance of Kontsevich's program on localizing the Fukaya category along a singular Lagrangian spine." @default.
• W2105600529 created "2016-06-24" @default.
• W2105600529 creator A5027075877 @default.
• W2105600529 creator A5048007436 @default.
• W2105600529 date "2018-04-30" @default.
• W2105600529 modified "2023-10-11" @default.
• W2105600529 title "Triangulated surfaces in triangulated categories" @default.
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• W2105600529 doi "https://doi.org/10.4171/jems/791" @default.
• W2105600529 hasPublicationYear "2018" @default.
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