Abstract
We study the Seiberg-Witten invariant λSW(X) of smooth spin 4 -manifolds X with the rational homology of S1 × S3 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 Frøyshov invariant h(X) and a certain Lefschetz number in the reduced monopole Floer homology of Kronheimer and Mrowka. We apply this formula to obstruct the existence of metrics of positive scalar curvature on certain 4 -manifolds, and to exhibit new classes of homology 3 -spheres of infinite order in the homology cobordism group.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2865-2942 |
| Number of pages | 78 |
| Journal | Geometry and Topology |
| Volume | 22 |
| Issue number | 5 |
| DOIs | |
| State | Published - Jun 1 2018 |
Keywords
- Frøyshov invariant
- Manifolds with periodic ends
- Monopole floer homology
- Seiberg-witten theory
ASJC Scopus subject areas
- Geometry and Topology
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Cite this
Lin, J., Ruberman, D., & Saveliev, N. (2018). A splitting theorem for the seiberg-witten invariant of a homology S1 × S3 Geometry and Topology, 22(5), 2865-2942. https://doi.org/10.2140/gt.2018.22.2865