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arXiv · 1806.00010

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

Yu Qiu
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Abstract

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.

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BibTeXRIS

Yu Qiu. 2018-05-31. Topological structure of spaces of stability conditions and topological Fukaya type categories. https://arxiv.org/abs/1806.00010

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