| Résume | Gauge theoretic invariants of a closed 4-manifold X usually are defined only in the setting where the intersection form has a non-zero positive part; this condition rules out reducible solutions. Many interesting questions remain, however, in the setting where the second homology is trivial. I will survey some recent work on finding invariants of such manifolds, and of new calculations. One approach is to use the Seiberg-Witten equations, and I will discuss a recent result on calculating these invariants, joint with Jianfeng Lin and Nikolai Saveliev. Time permitting, I will also explain a new Heegaard Floer invariant defined in joint work with Adam Levine. |
