English

Coordinates on the augmented moduli space of convex RP^2 structures

Differential Geometry 2021-09-17 v2 Geometric Topology

Abstract

Let S be an orientable, finite type surface with negative Euler characteristic. The augmented moduli space of convex real projective structures on S was first defined and topologized by the first author. In this article, 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 S. Using this, we give a simpler proof of the fact that the augmented moduli space of convex real projective structures on S 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 S.

Keywords

Cite

@article{arxiv.1812.11389,
  title  = {Coordinates on the augmented moduli space of convex RP^2 structures},
  author = {John Loftin and Tengren Zhang},
  journal= {arXiv preprint arXiv:1812.11389},
  year   = {2021}
}

Comments

45 pages, 18 figures, 1 appendix

R2 v1 2026-06-23T06:58:49.050Z