  We say that a complex analytic space, $X$, is an intersection cohomology
manifold if and only if the shifted constant sheaf on $X$ is isomorphic to
intersection cohomology; this is quickly seen to be equivalent to $X$ being a
homology manifold. Given an analytic function $f$ on an intersection cohomology
manifold, we describe a simple relation between $V(f)$ being an intersection
cohomology manifold and the vanishing cycle Milnor monodromy of $f$. We then
describe how the Sebastiani-Thom isomorphism allows us to easily produce
intersection cohomology manifolds with arbitrary singular sets. Finally, as an
easy application, we obtain restrictions on the cohomology of the Milnor fiber
of a hypersurface with a special type of one-dimensional critical locus.
