the smooth 4-dimensional poincare conjecture is something of an orphan. no significant progress has been made in a while, and no one is even really sure whether it's true or false. some plausible counterexamples have been known for over 20 years, and i'll tell you about a particular family of these, the cappell-shaneson spheres, which we've recently been thinking about again. the obvious approach to a counterexample is to find an invariant which distinguishes it from the standard 4-sphere; sadly no such invariants are known. we're taking a different approach by extracting a `local' problem, involving the slice genus of certain knots and links. rasmussen's $s$-invariant, related to the khovanov homology of a link, gives bounds on the slice genus, and thence a potential obstruction. unfortunately, the links are huge, and calculating the s-invariant is hard. nevertheless we've made some progress (a potientially dangerous shortcut, a new algorithm, and a new method of extracting the s-invariant), and even have an answer in one case. (with michael freedman, robert gompf and kevin walker)