Smooth structures on four-manifolds with finite cyclic fundamental groups
Abstract
For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z4m+2 and odd intersection form, with possibly seven exceptions, either admits no smooth structure or admits infinitely many distinct smooth structures up to diffeomorphism. Moreover, we construct infinite families of non-complex irreducible fake projective planes with diverse fundamental groups.
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