Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant

Tomasz Mrowka, Daniel Ruberman, Nikolai Saveliev

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We introduce a gauge-theoretic integer valued lift of the Rohlin invariant of a smooth 4-manifold X with the homology of S1×S3. The invariant has two terms: one is a count of solutions to the Seiberg-Witten equations on X, and the other is essentially the index of the Dirac operator on a non-compact manifold with end modeled on the infinite cyclic cover of X. Each term is metric (and perturbation) dependent, and we show that these dependencies cancel as the metric and perturbation vary in a generic 1-parameter family.

Original languageEnglish (US)
Pages (from-to)333-377
Number of pages45
JournalJournal of Differential Geometry
Volume88
Issue number2
StatePublished - Jun 2011

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Dirac Operator
Perturbation
Metric
Noncompact Manifold
Invariant
4-manifold
Cancel
Term
Homology
Gauge
Count
Vary
Cover
Integer
Dependent
Family

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant. / Mrowka, Tomasz; Ruberman, Daniel; Saveliev, Nikolai.

In: Journal of Differential Geometry, Vol. 88, No. 2, 06.2011, p. 333-377.

Research output: Contribution to journalArticle

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