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Monodromy groups of CP1-structures on punctured surfaces

Gupta, S (2021) Monodromy groups of CP1-structures on punctured surfaces. In: Journal of Topology, 14 (2). pp. 538-559.

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Official URL: https://doi.org/10.1112/topo.12189


For a punctured surface (Formula presented.), we characterize the representations of its fundamental group into (Formula presented.) that arise as the monodromy of a meromorphic projective structure on (Formula presented.) with poles of order at most two and no apparent singularities. This proves the analogue of a theorem of Gallo�Kapovich�Marden concerning (Formula presented.) -structures on closed surfaces, and settles a long-standing question about characterizing monodromy groups for the Schwarzian equation on punctured spheres. The proof involves a geometric interpretation of the Fock�Goncharov coordinates of the moduli space of framed (Formula presented.) -representations, following ideas of Thurston and some recent results of Allegretti�Bridgeland. © 2021 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

Item Type: Journal Article
Publication: Journal of Topology
Publisher: John Wiley and Sons Ltd
Additional Information: The copyright for this article belongs to John Wiley and Sons Ltd
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 30 Aug 2021 10:11
Last Modified: 30 Aug 2021 10:11
URI: http://eprints.iisc.ac.in/id/eprint/69497

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