Abstract
It is shown that every closed, simply connected topological 4-manifold having an odd intersection pairing, with the possible exception of the fake C P 2, admits an involution. We show that in many cases the involutions described here can be constructed to be locally linear, provided the Kirby-Siebenmann triangulation obstruction vanishes. It remains an open question, reduced to a question about characteristic elements of quadratic forms, whether this is true in general.
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