Geodesic
Triangulated surfaces in triangulated categories
Journal of the European Mathematical Society, Tome 20 (2018) no. 6, pp. 1473-1524.

Voir la notice de l'article provenant de la source EMS Press

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
Mots-clés : Triangulated categories, ribbon graphs, topological Fukaya categories, mapping class groups 
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     author = {Tobias Dyckerhoff and Mikhail Kapranov},
     title = {Triangulated surfaces in triangulated categories},
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     pages = {1473--1524},
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     year = {2018},
     doi = {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. https://geodesic-test.mathdoc.fr/articles/10.4171/jems/791/

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