Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Monodromy representations of meromorphic projective structures
HTML articles powered by AMS MathViewer

by Subhojoy Gupta and Mahan Mj PDF
Proc. Amer. Math. Soc. 148 (2020), 2069-2078 Request permission


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.
  • Dylan Allegretti and Tom Bridgeland, The monodromy of meromorphic projective structures, preprint, arXiv:1802.02505, 2019.
  • Dylan Gregory Lucasi Allegretti, The Geometry of Cluster Varieties from Surfaces, ProQuest LLC, Ann Arbor, MI, 2016. Thesis (Ph.D.)–Yale University. MR 3553669
  • M. Bestvina, K. Bromberg, K. Fujiwara, and J. Souto, Shearing coordinates and convexity of length functions on Teichmüller space, Amer. J. Math. 135 (2013), no. 6, 1449–1476. MR 3145000, DOI 10.1353/ajm.2013.0049
  • Vladimir Fock and Alexander Goncharov, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci. 103 (2006), 1–211. MR 2233852, DOI 10.1007/s10240-006-0039-4
  • V. V. Fock and A. B. Goncharov, The quantum dilogarithm and representations of quantum cluster varieties, Invent. Math. 175 (2009), no. 2, 223–286. MR 2470108, DOI 10.1007/s00222-008-0149-3
  • Daniel Gallo, Michael Kapovich, and Albert Marden, The monodromy groups of Schwarzian equations on closed Riemann surfaces, Ann. of Math. (2) 151 (2000), no. 2, 625–704. MR 1765706, DOI 10.2307/121044
  • Subhojoy Gupta and Mahan Mj, Meromorphic projective structures, grafting and the monodromy map, preprint, arXiv:1904.03804, 2019.
  • Subhojoy Gupta, Harmonic maps and wild Teichmüller spaces, Journal of Topology and Analysis (to appear), arXiv:1708.04780, 2017.
  • Subhojoy Gupta, Monodromy groups of $\mathbb {C}\mathrm {P}^1$-structures on punctured surfaces, in preparation.
  • John H. Hubbard, The monodromy of projective structures, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978) Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 257–275. MR 624819
  • Yoshinobu Kamishima and Ser P. Tan, Deformation spaces on geometric structures, Aspects of low-dimensional manifolds, Adv. Stud. Pure Math., vol. 20, Kinokuniya, Tokyo, 1992, pp. 263–299. MR 1208313, DOI 10.2969/aspm/02010263
  • F. Palesi, Introduction to positive representations and Fock-Goncharov coordinates, lecture notes,, 2013.
  • Yasutaka Sibuya, Global theory of a second order linear ordinary differential equation with a polynomial coefficient, North-Holland Mathematics Studies, Vol. 18, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. MR 0486867
  • W. P. Thurston, The geometry and topology of 3-manifolds, Princeton University Notes, 1980.
Similar Articles
Additional Information
  • Subhojoy Gupta
  • Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore, India
  • MR Author ID: 1001472
  • Email:
  • Mahan Mj
  • Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
  • MR Author ID: 606917
  • Email:
  • 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
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 2069-2078
  • MSC (2010): Primary 30F30, 57M50; Secondary 34M03, 30F60
  • DOI:
  • MathSciNet review: 4078090