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Monodromy representations of meromorphic projective structures

Authors: Subhojoy Gupta and Mahan Mj
Journal: Proc. Amer. Math. Soc. 148 (2020), 2069-2078
MSC (2010): Primary 30F30, 57M50; Secondary 34M03, 30F60
Published electronically: January 6, 2020
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Abstract: We determine the image of the monodromy map for meromorphic projective structures with poles of orders greater than two. This proves the analogue of a theorem of Gallo-Kapovich-Marden and answers a question of Allegretti and Bridgeland in this case. Our proof uses coordinates on the moduli space of framed representations arising from the work of Fock and Goncharov.

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Additional Information

Subhojoy Gupta
Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore, India

Mahan Mj
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India

Keywords: Projective structures on surfaces, meromorphic quadratic differentials, decorated character variety.
Received by editor(s): June 20, 2019
Received by editor(s) in revised form: August 29, 2019, and September 13, 2019
Published electronically: January 6, 2020
Additional Notes: The first author acknowledges the SERB, DST (Grant no. MT/2017/000706), the UGC Center for Advanced Studies grant, and the Infosys Foundation for their support.
Research of the second author was partly supported by a DST JC Bose Fellowship, Matrics research project grant MTR/2017/000005, and CEFIPRA project No. 5801-1. The second author was also partially supported by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund.
Communicated by: Kenneth Bromberg
Article copyright: © Copyright 2019 American Mathematical Society