SEIBERG-WITTEN THEORY AND Z/2^{p} ACTIONS ON SPIN 4-MANIFOLDS

JIM BRYAN

Abstract. Furuta’s ten-eighth’s 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 Z/2^{p} action, his 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 actions of Pin(2) and Z/2^{p} on the Seiberg-Witten moduli space. Our techniques also provide a simplification of the proof of Furuta’s theorem.