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

Jianfeng Lin, Daniel Ruberman, Nikolai Saveliev

Research output: Contribution to journalArticle

1 Citation (Scopus)

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

Fingerprint

Seiberg-Witten Invariants
Homology
4-manifold
Monopole
Theorem
Lefschetz number
Positive Scalar Curvature
Floer Homology
Cobordism
Invariant
Signed
Count
Metric
Term

Keywords

  • Frøyshov invariant
  • Manifolds with periodic ends
  • Monopole floer homology
  • Seiberg-witten theory

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

A splitting theorem for the seiberg-witten invariant of a homology S1 × S3 . / Lin, Jianfeng; Ruberman, Daniel; Saveliev, Nikolai.

In: Geometry and Topology, Vol. 22, No. 5, 01.06.2018, p. 2865-2942.

Research output: Contribution to journalArticle

Lin, Jianfeng ; Ruberman, Daniel ; Saveliev, Nikolai. / A splitting theorem for the seiberg-witten invariant of a homology S1 × S3 In: Geometry and Topology. 2018 ; Vol. 22, No. 5. pp. 2865-2942.
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