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April 2020 Parabolic vector bundles on Klein surfaces
Indranil Biswas, Florent Schaffhauser
Illinois J. Math. 64(1): 105-118 (April 2020). DOI: 10.1215/00192082-8165614

Abstract

Given a discrete subgroup Γ of finite co-volume of PGL(2,R), we define and study parabolic vector bundles on the quotient Σ of the (extended) hyperbolic plane by Γ. If Γ contains an orientation-reversing isometry, then the above is equivalent to studying real and quaternionic parabolic vector bundles on the orientation cover of degree two of Σ. We then prove that isomorphism classes of polystable real and quaternionic parabolic vector bundles are in a natural bijective correspondence with the equivalence classes of real and quaternionic unitary representations of Γ. Similar results are obtained for compact-type real parabolic vector bundles over Klein surfaces.

Citation

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Indranil Biswas. Florent Schaffhauser. "Parabolic vector bundles on Klein surfaces." Illinois J. Math. 64 (1) 105 - 118, April 2020. https://doi.org/10.1215/00192082-8165614

Information

Received: 23 April 2019; Revised: 31 October 2019; Published: April 2020
First available in Project Euclid: 6 March 2020

zbMATH: 07179192
MathSciNet: MR4072644
Digital Object Identifier: 10.1215/00192082-8165614

Subjects:
Primary: 14H60
Secondary: 30F35

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 1 • April 2020
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