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Pseudo-developing maps for ideal triangulations II: Positively oriented ideal triangulations of cone-manifolds

Alex Casella Feng Luo Stephan Tillmann

Geometric Analysis and Geometric Topology mathscidoc:1912.43808

Proceedings of the American Mathematical Society, 145, (8), 3543-3560, 2017
We generalise work of Young-Eun Choi to the setting of ideal triangulations with vertex links of arbitrary genus, showing that the set of all (possibly incomplete) hyperbolic cone-manifold structures realised by positively oriented hyperbolic ideal tetrahedra on a given topological ideal triangulation and with prescribed cone angles at all edges is (if non-empty) a smooth complex manifold of dimension the sum of the genera of the vertex links. Moreover, we show that the complex lengths of a collection of peripheral elements give a local holomorphic parameterisation of this manifold.
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@inproceedings{alex2017pseudo-developing,
  title={Pseudo-developing maps for ideal triangulations II: Positively oriented ideal triangulations of cone-manifolds},
  author={Alex Casella, Feng Luo, and Stephan Tillmann},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205927239085372},
  booktitle={Proceedings of the American Mathematical Society},
  volume={145},
  number={8},
  pages={3543-3560},
  year={2017},
}
Alex Casella, Feng Luo, and Stephan Tillmann. Pseudo-developing maps for ideal triangulations II: Positively oriented ideal triangulations of cone-manifolds. 2017. Vol. 145. In Proceedings of the American Mathematical Society. pp.3543-3560. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205927239085372.
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