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arXiv · 1609.04560

Schottky groups and maximal representations

Jean-Philippe Burelle·Nicolaus Treib
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Abstract

We describe a construction of Schottky type subgroups of automorphism groups of partially cyclically ordered sets. We apply this construction to the Shilov boundary of a Hermitian symmetric space and show that in this setting Schottky subgroups correspond to maximal representations of fundamental groups of surfaces with boundary. As an application, we construct explicit fundamental domains for the action of maximal representations into $\mathrm{Sp}(2n,\mathbb{R})$ on $\mathbb{RP}^{2n-1}$.

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Jean-Philippe Burelle, Nicolaus Treib. 2016-09-15. Schottky groups and maximal representations. https://doi.org/10.1007/s10711-017-0285-2

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