On the character variety of the four-holed sphere

  • Sara Maloni

    Brown University, Providence, USA
  • Frédéric Palesi

    Aix-Marseille Université, Marseille, France
  • Ser Peow Tan

    National University of Singapore, Singapore


We study the (relative) SL$(2, \mathbb C) character varieties of the four-holed sphere and the action of the mapping class group on them. We describe a domain of discontinuity for this action, and, in the case of real characters, show that this domain of discontinuity may be non-empty on the components where the relative Euler class is non-maximal.

Cite this article

Sara Maloni, Frédéric Palesi, Ser Peow Tan, On the character variety of the four-holed sphere. Groups Geom. Dyn. 9 (2015), no. 3, pp. 737–782

DOI 10.4171/GGD/326