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arXiv · 1607.04634

Topology of representation spaces of surface groups in PSL(2,R) with assigned boundary monodromy and nonzero Euler number

Gabriele Mondello
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Abstract

In this paper we complete the topological description of the space of representations of the fundamental group of a punctured surface in SL(2,R) with prescribed behavior at the punctures and nonzero Euler number, following the strategy employed by Hitchin in the unpunctured case and exploiting Hitchin-Simpson correspondence between flat bundles and Higgs bundles in the parabolic case. This extends previous results by Boden-Yokogawa and Nasatyr-Steer. A relevant portion of the paper is intended to give an overview of the subject.

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Gabriele Mondello. 2016-07-15. Topology of representation spaces of surface groups in PSL(2,R) with assigned boundary monodromy and nonzero Euler number. https://arxiv.org/abs/1607.04634

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