On smooth structures over $4$-manifolds with fundamental group of even order

Roberto Ladu; Simone Tagliente

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arXiv · 2603.29794

On smooth structures over $4$-manifolds with fundamental group of even order

Roberto Ladu·Simone Tagliente

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Abstract

We show that any topological, closed, oriented, non-spin $4$-manifold with fundamental group $\mathbb{Z}_{4k}$ and $\min(b_2^+, b_2^-)\geq 15$, has either none or infinitely many distinct smooth structures. Furthermore, we construct infinitely many non-diffeomorphic, irreducible, smooth structures on manifolds with signature zero, $b_2^+$ even and fundamental group $\mathbb{Z}_2\times G$, for any finite group $G$. This extends the results of Baykur-Stipsicz-Szab\'o.

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Roberto Ladu, Simone Tagliente. 2026-03-31. On smooth structures over $4$-manifolds with fundamental group of even order. https://arxiv.org/abs/2603.29794

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