Exotic non-orientable four-manifolds with prescribed fundamental group

Rafael Torres

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arXiv · 2508.19142

Exotic non-orientable four-manifolds with prescribed fundamental group

Rafael Torres

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Abstract

We show that any finitely presented group with an index two subgroup is realized as the fundamental group of a closed smooth non-orientable four-manifold that admits an exotic smooth structure, which is obtained by performing a Gluck twist. The orientation 2-covers of these four-manifolds are diffeomorphic. These two smooth structures remain inequivalent after adding arbitrarily many copies of the product of a pair of 2-spheres and stabilize after adding a single copy of the complex projective plane.

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BibTeX RIS

Rafael Torres. 2025-08-26. Exotic non-orientable four-manifolds with prescribed fundamental group. https://arxiv.org/abs/2508.19142

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