Irreducible exotic ${\mathbb {CP}}^2\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$'s with free involutions

R. İnanç Baykur; András I. Stipsicz; Zoltán Szabó

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arXiv · 2609.26450

Irreducible exotic ${\mathbb {CP}}^2\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$'s with free involutions

R. İnanç Baykur·András I. Stipsicz·Zoltán Szabó

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Abstract

We construct infinitely many pairwise non-diffeomorphic irreducible smooth four-manifolds homeomorphic to ${\mathbb {CP}}^2\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$, each admitting a free, orientation-preserving involution. Their quotients give infinitely many irreducible definite four-manifolds with fundamental group ${\mathbb {Z}}/2 {\mathbb {Z}}$ and $b_2=3$, filling the corresponding gap in the geography of such examples. The construction of infinitely many distinct examples relies on a novel equivariant torus surgery.

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BibTeX RIS

R. İnanç Baykur, András I. Stipsicz, Zoltán Szabó. 2026-09-22. Irreducible exotic ${\mathbb {CP}}^2\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$'s with free involutions. https://arxiv.org/abs/2609.26450

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