Seiberg-Witten equations, end-periodic Dirac operators, and a lift of Rohlin's invariant

Details Seiberg-Witten equations, end-periodic Dirac operators, and a lift of Rohlin's invariant Seiberg-Witten equations, end-periodic Dirac operators, and a lift of Rohlin's invariant

2009-05-27

arxiv.org/abs/0905.4319v3

Mathematics

Geometric Topology

Revision after referee report; section on negative definite manifolds revised. To appear in JDG

Scientific paper

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

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