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A
splitting theorem for the Seiberg-Witten invariant of a
homology $S^1 \times S^3$
Jianfeng Lin, Daniel Ruberman and Nikolai Saveliev |
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Geometry & Topology 22 (2018) 2865–2942
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Abstract |
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We study the Seiberg–Witten invariant of smooth spin –manifolds with the rational homology of 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 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 –manifolds, and to exhibit new classes of homology –spheres of infinite order in the homology cobordism group. |
Keywords
Seiberg–Witten theory, monopole Floer homology, Frøyshov
invariant, manifolds with periodic ends
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Mathematical Subject Classification 2010
Primary: 57R57, 57R58
Secondary: 53C21, 57M27, 58J28
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References |
Publication
Received: 7 March 2017
Accepted: 4 March 2018
Published: 1 June 2018
Proposed: Simon Donaldson
Seconded: András I Stipsicz, Ciprian Manolescu
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Authors |
| Jianfeng Lin | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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| Daniel Ruberman | |
| Department of Mathematics Brandeis University Waltham, MA United States |
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| Nikolai Saveliev | |
| Department of Mathematics University of Miami Coral Gables, FL United States |
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