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Bending fuchsian representations of fundamental groups of cusped surfaces in pu(2,1)

Pierre Will Institut Fourier

Differential Geometry mathscidoc:1609.10261

Journal of Differential Geometry, 90, (3), 473-520, 2012
We describe a new family of representations of 1() in PU(2,1), where  is a hyperbolic Riemann surface with at least one deleted point. This family is obtained by a bending process associated to an ideal triangulation of . We give an explicit description of this family by describing a coordinates system in the spirit of shear coordinates on the Teichm¨uller space. We identify within this family new examples of discrete, faithful, and type-preserving representations of 1(). In turn, we obtain a 1-parameter family of embeddings of the Teichm¨uller space of  in the PU(2,1)-representation variety of 1(). These results generalise to arbitrary  the results obtained in [42] for the 1-punctured torus.
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@inproceedings{pierre2012bending,
  title={BENDING FUCHSIAN REPRESENTATIONS OF FUNDAMENTAL GROUPS OF CUSPED SURFACES IN PU(2,1)},
  author={Pierre Will},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913224827179121923},
  booktitle={Journal of Differential Geometry},
  volume={90},
  number={3},
  pages={473-520},
  year={2012},
}
Pierre Will. BENDING FUCHSIAN REPRESENTATIONS OF FUNDAMENTAL GROUPS OF CUSPED SURFACES IN PU(2,1). 2012. Vol. 90. In Journal of Differential Geometry. pp.473-520. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913224827179121923.
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