A cohomological Seiberg-Witten invariant emerging from the adjunction inequality

Hokuto Konno

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arXiv · 1704.05859

A cohomological Seiberg-Witten invariant emerging from the adjunction inequality

Hokuto Konno

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Abstract

We construct an invariant of closed ${\rm spin}^c$ 4-manifolds using families of Seiberg-Witten equations. This invariant is formulated as a cohomology class on a certain abstract simplicial complex consisting of embedded surfaces of a 4-manifold. We also give examples of 4-manifolds which admit positive scalar curvature metrics and for which this invariant does not vanish. This non-vanishing result of our invariant provides a new class of adjunction-type genus constraints on configurations of embedded surfaces in a 4-manifold whose Seiberg-Witten invariant vanishes.

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Hokuto Konno. 2017-04-19. A cohomological Seiberg-Witten invariant emerging from the adjunction inequality. https://arxiv.org/abs/1704.05859

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