A deformation of penner's simplicial coordinate

Tian Yang Rutgers University

Differential Geometry mathscidoc:1609.10246

Journal of Differential Geometry, 89, (3), 529-551, 2011
We nd a one-parameter family of coordinates f hgh2R which is a deformation of Penner's simplicial coordinate of the decorated Teichmuller space of an ideally triangulated punctured surface (S; T) of negative Euler characteristic. If h > 0, the decorated Teichmuller space in the h coordinate becomes an explicit convex polytope P(T) independent of h, and if h < 0, the decorated Teichmuller space becomes an explicit bounded convex polytope Ph(T) so that Ph(T)  Ph0 (T) if h < h0. As a consequence, Bowditch-Epstein and Penner's cell decomposition of the decorated Teichmuller space is reproduced.
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@inproceedings{tian2011a,
  title={A DEFORMATION OF PENNER'S SIMPLICIAL COORDINATE},
  author={Tian Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913211510683287907},
  booktitle={Journal of Differential Geometry},
  volume={89},
  number={3},
  pages={529-551},
  year={2011},
}
Tian Yang. A DEFORMATION OF PENNER'S SIMPLICIAL COORDINATE. 2011. Vol. 89. In Journal of Differential Geometry. pp.529-551. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913211510683287907.
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