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Seiberg-Witten invariants of 4-dimensional homology circles


Speaker: Daniel Ruberman, Brandeis University
Location: 1147 MSB
Start time: Tue, Feb 6 2018, 1:10PM

Most applications of gauge theory in 4-dimensional topology are concerned with simply-connected manifolds with non-trivial second homology. I will discuss the opposite situation, first describing a Seiberg-Witten invariant for manifolds with first homology = Z and vanishing second homology; this invariant has an unusual index-theoretic correction term. I will discuss recent work with Jianfeng Lin and Nikolai Saveliev giving a new formula for this invariant in terms of monopole homology, and some applications.