Geometry and Topology Seminar

In the first talk we consider the SL(2,C)-character variety of
the four-holed sphere S, and the natural action of the mapping class group
MCG(S) on it. In particular, we describe a domain of discontinuity for the
action of MCG(S) on the relative character varieties, which is the set of
representations for which the traces of the boundary curves are fixed.
Time permitting, in the case of real characters, we show that this domain
of discontinuity may be non-empty on the components where the relative
Euler class is non-maximal.
I will focus on the combinatorial methods of the proofs.
(This is joint work with F. Palesi and S. P. Tan.)