A splitting theorem for the seiberg-witten invariant of a homology S1 × S3

Jianfeng Lin, Daniel Ruberman, Nikolai Saveliev

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1 Scopus citations

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 languageEnglish (US)
Pages (from-to)2865-2942
Number of pages78
JournalGeometry and Topology
Volume22
Issue number5
DOIs
StatePublished - 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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