Open Access
June 2011 Seiberg-Witten Equations, End-Periodic Dirac Operators, and a Lift of Rohlin's Invariant
Tomasz Mrowka, Daniel Ruberman, Nikolai Saveliev
J. Differential Geom. 88(2): 333-377 (June 2011). DOI: 10.4310/jdg/1320067650


We introduce a gauge-theoretic integer valued lift of the Rohlin invariant of a smooth 4-manifold $X$ with the homology of $S^1×S^3$. 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.


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Tomasz Mrowka. Daniel Ruberman. Nikolai Saveliev. "Seiberg-Witten Equations, End-Periodic Dirac Operators, and a Lift of Rohlin's Invariant." J. Differential Geom. 88 (2) 333 - 377, June 2011.


Published: June 2011
First available in Project Euclid: 31 October 2011

zbMATH: 1238.57028
MathSciNet: MR2838269
Digital Object Identifier: 10.4310/jdg/1320067650

Rights: Copyright © 2011 Lehigh University

Vol.88 • No. 2 • June 2011
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