Decorated marked surfaces II~Intersection numbers and dimensions of Homs

Yu Qiu Tsinghua University Yu Zhou Tsinghua University

Category Theory Representation Theory mathscidoc:1906.02002

Transactions of the American Mathematical Society, 372, 635-660 , 2019
We study derived categories arising from quivers with potential associated to a decorated marked surface S_Delta, in the sense taken in a paper by Qiu. We prove two conjectures from Qiu’s paper in which, under a bijection between certain objects in these categories and certain arcs in S, the dimensions of morphisms between these objects equal the intersection numbers between the corresponding arcs.
Calabi-Yau categories, decorated marked surfaces, Intersection numbers
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@inproceedings{yu2019decorated,
  title={Decorated marked surfaces II~Intersection numbers and dimensions of Homs},
  author={Yu Qiu, and Yu Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190625200543021868355},
  booktitle={Transactions of the American Mathematical Society},
  volume={372},
  pages={635-660 },
  year={2019},
}
Yu Qiu, and Yu Zhou. Decorated marked surfaces II~Intersection numbers and dimensions of Homs. 2019. Vol. 372. In Transactions of the American Mathematical Society. pp.635-660 . http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190625200543021868355.
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