Higher type adjunction inequalities for Donaldson invariants

Details Higher type adjunction inequalities for Donaldson invariants Higher type adjunction inequalities for Donaldson invariants

1999-01-11

arxiv.org/abs/math/9901046v2

Mathematics

Differential Geometry

21 pages, no figures, Latex2e

Scientific paper

We prove new adjunction inequalities for embedded surfaces in four-manifolds with non-negative self-intersection number by using the Donaldson invariants. These formulas are completely analogous to the ones obtained by Ozsv\'ath and Szab\'o using the Seiberg-Witten invariants. To prove these relations, we give a fairly explicit description of the structure of the Fukaya-Floer homology of a surface times a circle. As an aside, we also relate the Floer homology of a surface times a circle with the cohomology of some symmetric products of the surface.

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