Monodromy factorizations of Seifert fibered spaces

Abstract

We present relations in the mapping class monoid of $S_{0,0}^n$ between products of boundary parallel twists and those involving only non boundary parallel twists. These are of particular interest because each element gives an open book decomposition of a contact 3-manifold, and different factorizations of the same mapping class give potentially distinct symplectic fillings with diffeomorphic boundaries. We apply these results in order to compute the Euler characteristics of fillings resulting from different factorizations, present plumbing graphs for the fillings given by products of boundary parallel twists, and provide sharp bounds on the Euler characteristics for fillings arising from such relations.