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

## TL;DR

This paper provides explicit coordinate descriptions of the augmented moduli space of convex RP^2 structures on surfaces, simplifying the proof of its homeomorphism to an orbifold vector bundle over the Deligne-Mumford compactification.

## Contribution

It introduces explicit coordinates for the augmented moduli space and offers a simplified proof of its topological structure as an orbifold vector bundle.

## Key findings

- Explicit coordinates on the augmented moduli space are constructed.
- The topology of the augmented moduli space is described explicitly.
- A simplified proof of the homeomorphism to the orbifold vector bundle is provided.

## 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.