Mapping class group relations, Stein fillings, and planar open book decompositions, I

We will discuss using mapping class group techniques to  approach
the 'geography' problem for Stein fillings of a contact  3-manifold. We
will show how these techniques give an obstruction for  a contact three
manifold to admit a planar open book decomposition,  and through examples
demonstrate independence of this obstruction from  those previously
uncovered.