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

@article{Qiu2018TopologicalSO, title={Topological structure of spaces of stability conditions and topological Fukaya type categories}, author={Y. Qiu}, journal={arXiv: Representation Theory}, year={2018} }

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… Expand

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