Veech Groups and Triangulations of Half-Dilation Pillowcases

Taro Shima

Veech Groups and Triangulations of Half-Dilation Pillowcases

Geometric Topology 2022-05-03 v1

Authors: Taro Shima

Abstract

In this paper we consider the symmetries of triangulable half-dilation structures on the sphere with four singularities. We show that all such surfaces can be produced by a tetrahedral construction. Using this construction, we calculate each such surface's symmetry group in $\operatorname{PSL}(2, \mathbb{R})$ called the Veech group.

Keywords

veech group half-dilation structure triangulation sphere with four singularities tetrahedral construction psl(2,r)

Cite

@article{arxiv.2205.00100,
  title  = {Veech Groups and Triangulations of Half-Dilation Pillowcases},
  author = {Taro Shima},
  journal= {arXiv preprint arXiv:2205.00100},
  year   = {2022}
}

Comments

17 pages, 10 figures

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