Mathematical Research Letters

Volume 12 (2005)

Number 1

Coordinates for the moduli space of flat $PSL(2,\mathbb{R})$-connections

Pages: 23 – 36



R. M. Kashaev (Université de Genève)


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