Higher type adjunction inequalities for Donaldson invariants

Muñoz, Vicente

doi:10.1090/S0002-9947-01-02793-3

Higher type adjunction inequalities for Donaldson invariants
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Trans. Amer. Math. Soc. 353 (2001), 2635-2654 Request permission

Abstract:

We prove new adjunction inequalities for embedded surfaces in four-manifolds with non-negative self-intersection number using the Donaldson invariants. These formulas are completely analogous to the ones obtained by Ozsváth and Szabó 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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