The homology groups of the Milnor fiber associated to a central arrangement of hyperplanes in C3

We use covering space theory and the fundamental group of complements of complexified real line arrangements to explore the homology groups of the associated Milnor fiber. This work yields a combinatorially determined upper bound on the rank of the first homology group of the Milnor fiber. Under certain combinatorial conditions, we then show that one may determine the exact rank of the group and show that it is torsion free.