Allegretti, D.G.L. and Bridgeland, T. (2020) The monodromy of meromorphic projective structures. Transactions of the American Mathematical Society, 373. pp. 6321-6367. ISSN 0002-9947
Abstract
We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of framed $\mathrm{PGL}_2(\mathbb{C})$ local systems on the associated marked bordered surface. We prove that the image of this map is contained in the union of the domains of the cluster charts. We discuss a number of open questions concerning this monodromy map.
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Item Type: | Article | ||||||
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Copyright, Publisher and Additional Information: | © 2020 American Mathematical Society. This is an author-produced version of a paper subsequently published in Transactions of the American Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
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Keywords: | Geometric Topology (math.GT); Algebraic Geometry (math.AG); Differential Geometry (math.DG) | ||||||
Dates: |
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Institution: | The University of Sheffield | ||||||
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) | ||||||
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Depositing User: | Symplectic Sheffield | ||||||
Date Deposited: | 16 Feb 2018 16:15 | ||||||
Last Modified: | 17 Apr 2024 15:07 | ||||||
Status: | Published | ||||||
Publisher: | American Mathematical Society | ||||||
Refereed: | Yes | ||||||
Identification Number: | https://doi.org/10.1090/tran/8093 | ||||||
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