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Triangulated surfaces in triangulated categories

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 simp...

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publication date:
2013-06-11
Keywords:
Pubs id:
pubs:401197
UUID:
uuid:0a6911eb-3185-44a6-a406-881fbf6f11f7
Local pid:
pubs:401197
Source identifiers:
401197
Deposit date:
2013-11-16

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