Please use this identifier to cite or link to this item: https://doi.org/10.1112/jlms.12488
Title: Coordinates on the augmented moduli space of convex RP2 structures
Authors: Loftin, John
Zhang, Tengren 
Keywords: Science & Technology
Physical Sciences
Mathematics
53-02 (primary)
REAL PROJECTIVE-STRUCTURES
CUBIC DIFFERENTIALS
SURFACES
COMPACTIFICATION
Issue Date: 30-Jun-2021
Publisher: WILEY
Citation: Loftin, John, Zhang, Tengren (2021-06-30). Coordinates on the augmented moduli space of convex RP2 structures. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES 104 (4) : 1930-1972. ScholarBank@NUS Repository. https://doi.org/10.1112/jlms.12488
Abstract: Let (Formula presented.) be an orientable, finite-type surface with negative Euler characteristic. The augmented moduli space of convex real projective structures on (Formula presented.) was first defined and topologized by the first author. In this paper, we give an explicit description of this topology using explicit coordinates. More precisely, given every point in this augmented moduli space, we find explicit continuous coordinates on the quotient of a suitable open neighborhood about this point by a suitable subgroup of the mapping class group of (Formula presented.). Using this, we give a simpler proof of the fact that the augmented moduli space of convex real projective structures on (Formula presented.) is homeomorphic to the orbifold vector bundle of regular cubic differentials over the Deligne–Mumford compactification of the moduli space of Riemann surfaces homeomorphic to (Formula presented.).
Source Title: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
URI: https://scholarbank.nus.edu.sg/handle/10635/242961
ISSN: 0024-6107
1469-7750
DOI: 10.1112/jlms.12488
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