Simple geodesics and Markoff quads

Yi Huang Tsinghua University Paul Norbury University of Melbourne

Geometric Analysis and Geometric Topology Representation Theory arXiv subject: Geometric Topology (math.GT) mathscidoc:2206.15001

Geometriae Dedicata, 186, 113-148, 2016.8
The action of the mapping class group of the thrice-punctured projective plane on its GL(2,C) character variety produces an algorithm for generating the simple length spectra of quasi-Fuchsian thrice-punctured projective planes. We apply this algorithm to quasi-Fuchsian representations of the corresponding fundamental group to prove: a sharp upper-bound for the length its shortest geodesic, a McShane identity and the surprising result of non-polynomial growth for the number of simple closed geodesic lengths.
Riemann surfaces, hyperbolic surfaces, Teichmueller theory, McShane identity, simple geodesics
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@inproceedings{yi2016simple,
  title={Simple geodesics and Markoff quads},
  author={Yi Huang, and Paul Norbury},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220608151612653202343},
  booktitle={Geometriae Dedicata},
  volume={186},
  pages={113-148},
  year={2016},
}
Yi Huang, and Paul Norbury. Simple geodesics and Markoff quads. 2016. Vol. 186. In Geometriae Dedicata. pp.113-148. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220608151612653202343.
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