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Triangulated cores of punctured-torus groups

Francois Gueritaud Universit´e de Lille I,

Differential Geometry mathscidoc:1609.10090

Journal of Differential Geometry, 81, (1), 91-142, 2009
We show that the interior of the convex core of a quasifuchsian punctured-torus group admits an ideal decomposition (usually an infinite triangulation) which is canonical in two very different senses: in a combinatorial sense via the pleating invariants, and in a geometric sense via an Epstein-Penner convex hull construction in Minkowski space. This result re-proves the Pleating Lamination Theorem for quasifuchsian punctured-torus groups, and extends to all punctured-torus groups if a strong version of the Pleating Lamination Conjecture is true.
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@inproceedings{francois2009triangulated,
  title={TRIANGULATED CORES OF PUNCTURED-TORUS GROUPS},
  author={Francois Gueritaud},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909143019338344747},
  booktitle={Journal of Differential Geometry},
  volume={81},
  number={1},
  pages={91-142},
  year={2009},
}
Francois Gueritaud. TRIANGULATED CORES OF PUNCTURED-TORUS GROUPS. 2009. Vol. 81. In Journal of Differential Geometry. pp.91-142. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909143019338344747.
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