Meromorphic projective structures, grafting and the monodromy map

Gupta, S and Mahan, Mj (2021) Meromorphic projective structures, grafting and the monodromy map. In: Advances in Mathematics, 383 .

PDF adv_mat_384-04_2021.pdf - Published Version Restricted to Registered users only Download (1MB) | Request a copy

Abstract

A meromorphic projective structure on a punctured Riemann surface X�P is determined, after fixing a standard projective structure on X, by a meromorphic quadratic differential with poles of order three or more at each puncture in P. In this article we prove the analogue of Thurston's grafting theorem for such meromorphic projective structures, that involves grafting crowned hyperbolic surfaces. This also provides a grafting description for projective structures on C that have polynomial Schwarzian derivatives. As an application of our main result, we prove the analogue of a result of Hejhal, namely, we show that the monodromy map to the decorated character variety (in the sense of Fock-Goncharov) is a local homeomorphism. © 2021 Elsevier Inc.

Item Type:	Journal Article
Publication:	Advances in Mathematics
Publisher:	Academic Press Inc
Additional Information:	The copyright for this article belongs to Academic Press Inc
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	30 Mar 2021 05:54
Last Modified:	30 Mar 2021 05:54
URI:	http://eprints.iisc.ac.in/id/eprint/68575

Actions (login required)

View Item