Smooth structures on four-manifolds with finite cyclic fundamental groups

R. Inanc Baykur; Andras I. Stipsicz; Zoltan Szabo

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arXiv · 2406.09007

Smooth structures on four-manifolds with finite cyclic fundamental groups

R. Inanc Baykur·Andras I. Stipsicz·Zoltan Szabo

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Abstract

For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z_{4m+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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BibTeX RIS

R. Inanc Baykur, Andras I. Stipsicz, Zoltan Szabo. 2024-06-13. Smooth structures on four-manifolds with finite cyclic fundamental groups. https://arxiv.org/abs/2406.09007

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