Abstract:
Furuta's ``10/8-th'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 action of a twisted product 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.