Contents Online
Mathematical Research Letters
Volume 12 (2005)
Number 1
Coordinates for the moduli space of flat $PSL(2,\mathbb{R})$-connections
Pages: 23 – 36
DOI: https://dx.doi.org/10.4310/MRL.2005.v12.n1.a3
Author
Abstract
Let $\mathcal{M}$ be the moduli space of irreducible flat $PSL(2,\mathbb{R})$ connections on a punctured surface of finite type with parabolic holonomies around punctures. By using a notion of \emph{admissibility} of an ideal arc, $\mathcal{M}$ is covered by dense open subsets associated to ideal triangulations of the surface. A principal bundle over $\mathcal{M}$ is constructed which, when restricted to the Teichmüller component of $\mathcal{M}$, is isomorphic to the decorated Teichmüller space of Penner. The construction gives a generalization to $\mathcal{M}$ of Penner’s coordinates for the Teichmüller space.
Published 1 January 2005