On Fenchel-Nielsen Coordinates of Surface Group Representations into SU(3,1)

Krishnendu Gongopadhyay; Shiv Parsad

On Fenchel-Nielsen Coordinates of Surface Group Representations into SU(3,1)

Geometric Topology 2017-01-10 v3

Authors: Krishnendu Gongopadhyay , Shiv Parsad

Abstract

Let $\Sigma_g$ be a compact, connected, orientable surface of genus $g \geq 2$ . We ask for a parametrization of the discrete, faithful, totally loxodromic representations in the deformation space ${\rm Hom}(\pi_1(\Sigma_g), {\rm SU}(3,1))/{\rm SU}(3,1)$ . We show that such a representation, under some hypothesis, can be determined by $30g-30$ real parameters.

Keywords

fenchel-nielsen coordinates surface group representations su(3,1) deformation space loxodromic representations teichmuller theory hyperbolic geometry

Cite

@article{arxiv.1411.6755,
  title  = {On Fenchel-Nielsen Coordinates of Surface Group Representations into SU(3,1)},
  author = {Krishnendu Gongopadhyay and Shiv Parsad},
  journal= {arXiv preprint arXiv:1411.6755},
  year   = {2017}
}

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Corrected typos, updated bibliography

On Fenchel-Nielsen Coordinates of Surface Group Representations into SU(3,1)

Abstract

Keywords

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