Combinatorial methods on actions on character varieties
Sara Maloni (Brown)
Abstract: In this talk we consider the SL(2,C)--character variety X =
Hom(\pi_1(S),SL(2,C))//SL(2,C) 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 X_{(a,b,c,d)}, 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. (This is a
joint work with F. Palesi and S. P. Tan.)
I will recall all the basic definitions and focus on the combinatorial
methods of the proofs.