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

• Main Authors: Mrowka, Tomasz S. (Contributor), Ruberman, Daniel (Author), Saveliev, Nikolai (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: International Press of Boston, Inc., 2013-09-11T18:02:09Z.
• Subjects: Article
• Online Access: Get fulltext

Author Manuscript: 4 Apr 2011
We introduce a gauge-theoretic integer valued lift of the Rohlin invariant of a smooth 4-manifold X with the homology of S[superscript 1]×S[superscript 3]. 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.