On the Milnor Fiber Boundary of a Quasi-Ordinary Surface

We give a recursive formula, expressed in terms of the characteristic tuples, for the Betti numbers of the boundary of the Milnor fiber of an irreducible quasi-ordinary surface. The singular locus of the surface consists of two components, and for each component we introduce a sequence of increasingly simpler surfaces. Our recursion depends on a detailed comparison of these two sequences. In the final section, we indicate how we expect pieces of these associated surfaces to glue together to reconstruct the Milnor fiber and its boundary.