Comparing gauge theoretic invariants of homology S^1 x S^3
Location
While classical gauge theoretic invariants for 4-manifolds are usually defined in the setting that the intersection form has nontrivial positive part, there are several invariants for a 4-manifold X with the homology S^1 x S^3. The first one is the Casson-Seiberg-Witten invariant LSW(X) defined by Mrowka-Ruberman-Saveliev; the second one is the Furuta-Ohta invariant LFO(X). It is conjectured that these two invariants are equal to each other (This is an analogue of Witten’s conjecture relating Donaldson and Seiberg-Witten invariants.)
In this talk, I will recall the definition of these two invariants, give some applications of them and sketch a prove of this conjecture for finite-order mapping tori. This is based on a joint work with Danny Ruberman and Nikolai Saveliev.