$L^2$ harmonic forms and the Seiberg-Witten map on non compact four manifolds

preprint2020arXivOpen access

We explain a new phenomenon on non compact complete Riemannian four manifolds, where d^+ image of one forms can not exhaust densely on L^2 self dual forms on each compact subset, if a certain L^2 self dual harmonic form exists. This leads to construct a new functional analytic framework on the Seiberg-Witten map.

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$L^2$ harmonic forms and the Seiberg-Witten map on non compact four manifolds

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$L^2$ harmonic forms and the Seiberg-Witten map on non compact four manifolds