It is certainly well-known that a suitable count of solutions to the Yang-Mills or SeibergWitten equations gives rise to invariants of a smooth 4-manifold. In recent years, these invariants haveâ€¦ (More)

Let X be a Z[Z]â€“homology S1 Ã— S3, that is, a smooth closed oriented 4manifold such that Hâˆ—(X;Z) = Hâˆ—(S 1 Ã— S3;Z) and Hâˆ—(XÌƒ;Z) = Hâˆ—(S 3;Z), where XÌƒ is the universal abelian cover of X. Denote byâ€¦ (More)

This article surveys our ongoing project about the relationship between invariants extending the classical Rohlin invariant of homology spheres and those coming from 4â€“dimensional (Yang-Mills) gaugeâ€¦ (More)

If the Bing double of a knot K is slice, then K is algebraically slice. In addition the Heegaardâ€“Floer concordance invariants Ï„ , developed by OzsvÃ¡th-SzabÃ³, and Î´, developed by Manolescu and Owens,â€¦ (More)

This paper studies Dirac operators on end-periodic spin manifolds of dimension at least 4. We provide a necessary and sufficient condition for such an operator to be Fredholm for a genericâ€¦ (More)

One of the striking initial applications of the Seiberg-Witten invariants was to give new obstructions to the existence of Riemannian metrics of positive scalar curvature on 4â€“ manifolds. Theâ€¦ (More)

We use a 1â€“parameter version of gauge theory to investigate the topology of the diffeomorphism group of 4â€“manifolds. A polynomial invariant, analogous to the Donaldson polynomial, is defined, and isâ€¦ (More)

We study the space of positive scalar curvature (psc) metrics on a 4â€“manifold, and give examples of simply connected manifolds for which it is disconnected. These examples imply that concordance ofâ€¦ (More)