arXiv:1806.00010 Abstract | arXiv Analytics

arXiv:1806.00010 [math.RT]Abstract References Reviews Resources

Topological structure of spaces of stability conditions and topological Fukaya type categories

Published 2018-05-31Version 1

This is a survey on two closely related subjects. First, we review the study of topological structure of `finite type' components of spaces of Bridgeland's stability conditions on triangulated categories. The key is to understand Happel-Reiten-Smalo tilting as tiling of cells. Second, we review topological realizations of various Fukaya type categories, namely cluster/Calabi-Yau and derived categories from surfaces. The corresponding spaces of stability conditions are of `tame' nature and can be realized as moduli spaces of quadratic differentials due to Bridgeland-Smith and Haiden-Katzarkov-Kontsevich.

Comments: This survey is contributed to the proceedings of the first annual meeting of ICCM

Categories: math.RT, math.AG, math.GT

Keywords: topological fukaya type categories, topological structure, bridgelands stability conditions, quadratic differentials, finite type

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