Dynamics of the mapping class group on the moduli of a punctured sphere with rational holonomy

Joseph P. Previte, Eugene Z. Xia

Let $M$ be a four-holed sphere and $\Gamma$ the mapping class group of $M$ fixing the boundary $\partial M$. The group $\Gamma$ acts on $M_B(SL(2,C))=Ho{m}_B^{+}(p{i}_1(M),SL(2,C))/SL(2,C)$ whic…