Smooth structures on four-manifolds with finite cyclic fundamental groups

2024/06/13 by R. İnanç Baykur, András I. Stipsicz, Baykur, R. Inanc +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2406.09007

openalex publication_date 2024/06/13 · openalex created_date 2024/06/15 · openalex updated_date 2026/07/28

Abstract

For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z_4m+2 and odd intersection form, with possibly seven exceptions, either admits no smooth structure or admits infinitely many distinct smooth structures up to diffeomorphism. Moreover, we construct infinite families of non-complex irreducible fake projective planes with diverse fundamental groups.

Related

• Non-smoothable four-manifolds with cyclic fundamental group
• Definite four-manifolds with exotic smooth structures
• Exotic definite four-manifolds with non-cyclic fundamental group
• Exotic definite four-manifolds with non-trivial fundamental group
• Smooth manifolds with infinite fundamental group admitting no real\n projective structure