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. 737–782DOI 10.4171/GGD/326