Geodesic
Triangulated surfaces in triangulated categories
Journal of the European Mathematical Society, Tome 20 (2018) no. 6, pp. 1473-1524 Cet article a éte moissonné depuis la source EMS Press

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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 of 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.
DOI : 10.4171/jems/791
Classification : 18-XX, 14-XX
Keywords: Triangulated categories, ribbon graphs, topological Fukaya categories, mapping class groups 
@article{JEMS_2018_20_6_a3,
     author = {Tobias Dyckerhoff and Mikhail Kapranov},
     title = {Triangulated surfaces in triangulated categories},
     journal = {Journal of the European Mathematical Society},
     pages = {1473--1524},
     year = {2018},
     volume = {20},
     number = {6},
     doi = {10.4171/jems/791},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/791/}
}
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Tobias Dyckerhoff; Mikhail Kapranov. Triangulated surfaces in triangulated categories. Journal of the European Mathematical Society, Tome 20 (2018) no. 6, pp. 1473-1524. doi: 10.4171/jems/791

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