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Finite presentations for spherical/braid twist groups from decorated marked surfaces

Yu Qiu Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084 China Yu Zhou Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084 China

Geometric Analysis and Geometric Topology Representation Theory mathscidoc:2204.15001

Journal of Topology, 13, 501-538, 2020.3
We give a finite presentation for the braid twist group of a decorated surface. If the decorated surface arises from a triangulated marked surface without punctures, we obtain a finite presentation for the spherical twist group of the associated 3-Calabi–Yau triangulated category. The motivation/application is that the result will be used to show that the (principal component of) space of stability conditions on the 3-Calabi–Yau category is simply connected in the sequel [King and Qiu, Invent. Math., to appear].
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@inproceedings{yu2020finite,
  title={Finite presentations for spherical/braid twist groups from decorated marked surfaces},
  author={Yu Qiu, and Yu Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429162456938999173},
  booktitle={Journal of Topology},
  volume={13},
  pages={501-538},
  year={2020},
}
Yu Qiu, and Yu Zhou. Finite presentations for spherical/braid twist groups from decorated marked surfaces. 2020. Vol. 13. In Journal of Topology. pp.501-538. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429162456938999173.
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