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- W2589106366 abstract "We study the Seiberg-Witten invariant $lambda_{rm{SW}} (X)$ of smooth spin $4$-manifolds $X$ with integral homology of $S^1times S^3$ defined by Mrowka, Ruberman, and Saveliev as a signed count of irreducible monopoles amended by an index-theoretic correction term. We prove a splitting formula for this invariant in terms of the Fr{o}yshov invariant $h(X)$ and a certain Lefschetz number in the reduced monopole Floer homology of Kronheimer and Mrowka. We apply this formula to obstruct existence of metrics of positive scalar curvature on certain 4-manifolds, and to exhibit new classes of integral homology $3$-spheres of Rohlin invariant one which have infinite order in the homology cobordism group." @default.
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- W2589106366 date "2018-06-01" @default.
- W2589106366 modified "2023-10-03" @default.
- W2589106366 title "A splitting theorem for the Seiberg-Witten invariant of a homology S1× S3" @default.
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- W2589106366 doi "https://doi.org/10.2140/gt.2018.22.2865" @default.
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