Topology of representation spaces of surface groups in PSL(2,R) with assigned boundary monodromy and nonzero Euler number
arXiv:1607.04634
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.
37 pages; revised version: small mistake in the main statement and some inaccuracies are now corrected, credits added