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

Krishnendu Gongopadhyay; Shiv Parsad

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arXiv · 1411.6755

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

Krishnendu Gongopadhyay·Shiv Parsad

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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.

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Krishnendu Gongopadhyay, Shiv Parsad. 2014-11-25. On Fenchel-Nielsen Coordinates of Surface Group Representations into SU(3,1). https://arxiv.org/abs/1411.6755

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