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.

Topology of representation spaces of surface groups in PSL2(R) with assigned boundary monodromy and nonzero Euler number / Mondello, G. - In: PURE AND APPLIED MATHEMATICS QUARTERLY. - ISSN 1558-8599. - STAMPA. - 12:3(2018), pp. 399-462. [10.4310/PAMQ.2016.v12.n3.a3]

Topology of representation spaces of surface groups in PSL2(R) with assigned boundary monodromy and nonzero Euler number

Mondello, G
2018

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.
2018
representation spaces; Euler number; parabolic Higgs bundles; uniformization
01 Pubblicazione su rivista::01a Articolo in rivista
Topology of representation spaces of surface groups in PSL2(R) with assigned boundary monodromy and nonzero Euler number / Mondello, G. - In: PURE AND APPLIED MATHEMATICS QUARTERLY. - ISSN 1558-8599. - STAMPA. - 12:3(2018), pp. 399-462. [10.4310/PAMQ.2016.v12.n3.a3]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1083794
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