Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant
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Mrowka_Seiberg-witten equations.pdf
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Author(s)
Mrowka, Tomasz S.
Ruberman, Daniel
Saveliev, Nikolai
Date Issued
June 2011
Journal
Journal of Differential Geometry
Publisher
International Press of Boston, Inc.
Citation
Mrowka, Tomasz et al. “Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant.” Journal of Differential Geometry 88 (2011): 333–377.
Version
Author's final manuscript
Abstract
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.
Description
Author Manuscript: 4 Apr 2011
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&page=toc&handle=euclid.jdg/1320067645
