Seiberg-Witten theory and $\znums /2^{p}$ actions on spin $4$-manifolds

Furuta’s “10/8ths” theorem gives a bound on the magnitude of the signature of a smooth spin 4-manifold in terms of the second Betti number. We show that, in the presence of a $\Zp $ action, this bound can be strengthened. As applications, we give new genus bounds on classes with divisibility, and we give a classification of involutions on rational cohomology $K3$'s. We utilize the action of $\operatorname{Pin}{(2)}\Tilde{\times }\Zp $ on the Seiberg-Witten moduli space. Our techniques also provide a simplification of the proof of Furuta’s theorem.

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Published 1 January 1998