New Exotic four-manifolds with $\mathbb{Z}/2\mathbb{Z}$ fundamental group

Márton Beke; László Koltai; Sarah Zampa

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arXiv · 2312.08452

New Exotic four-manifolds with $\mathbb{Z}/2\mathbb{Z}$ fundamental group

Márton Beke·László Koltai·Sarah Zampa

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Abstract

We extend a construction of Stipsicz-Szab\'{o} of infinitely many irreducible exotic smooth structures of some closed four-manifolds with even $b_2^+$ and fundamental group $\mathbb{Z}/2\mathbb{Z}$. We use the double node surgery and rational blow down constructions of Fintushel-Stern on some elliptic fibrations equipped with a free involution. The construction is done in an equivariant manner and the factor manifolds are distinguished by the Seiberg-Witten invariants of their universal covers.

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Márton Beke, László Koltai, Sarah Zampa. 2023-12-13. New Exotic four-manifolds with $\mathbb{Z}/2\mathbb{Z}$ fundamental group. https://arxiv.org/abs/2312.08452

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