Coordinates on the augmented moduli space of convex RP2 structures

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.).