The 10/8-conjecture and equivariant e(C)-invariants

Abstract

Let X be a smooth closed oriented non-spin 4-manifold with even intersection form kE(8) circle plus nH (ngreater than or equal to1). The 10/8-conjecture states that n is greater than or equal to \k\. In this paper we give a proof of the 10/8-conjecture. The strategy of this paper is to use the finite dimensional approximation of the map induced from the Seiberg-Witten equations and equivariant e(C)-invariants as in the paper of M. Furuta and Y. Kametani.