Exotic non-orientable four-manifolds with prescribed fundamental group

2025/08/26 by Torres, Rafael
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2508.19142

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.

Citations

• Stably exotic 4-manifolds
• Smooth structures on non-orientable four-manifolds and free involutions

Cited by

• Stably exotic 4-manifolds

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