Decorated marked surfaces: spherical twists versus braid twists

Yu Qiu Tsinghua University

Representation Theory mathscidoc:1906.02003

Mathematische Annalen, 365, 595–633, 2016
We are interested in the 3-Calabi-Yau categories D arising from quivers with potential associated to a triangulated marked surface S (without punctures). We prove that the spherical twist group ST of D is isomorphic to a subgroup (generated by braid twists) of the mapping class group of the decorated marked surface S_Delta. Here S_Delta is the surface obtained from S by decorating with a set of points, where the number of points equals the number of triangles in any triangulations of S. For instance, when S is an annulus, the result implies that the corresponding spaces of stability conditions on D are contractible.
Calabi-Yau categories, spherical twists, quivers with potential, braid group, stability conditions
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@inproceedings{yu2016decorated,
  title={Decorated marked surfaces: spherical twists versus braid twists},
  author={Yu Qiu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190625201040038931356},
  booktitle={Mathematische Annalen},
  volume={365},
  pages={595–633},
  year={2016},
}
Yu Qiu. Decorated marked surfaces: spherical twists versus braid twists. 2016. Vol. 365. In Mathematische Annalen. pp.595–633. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190625201040038931356.
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