English

Smooth structures on four-manifolds with finite cyclic fundamental groups

Geometric Topology 2024-06-14 v1 Differential Geometry

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.

Keywords

Cite

@article{arxiv.2406.09007,
  title  = {Smooth structures on four-manifolds with finite cyclic fundamental groups},
  author = {R. Inanc Baykur and Andras I. Stipsicz and Zoltan Szabo},
  journal= {arXiv preprint arXiv:2406.09007},
  year   = {2024}
}

Comments

32 pages

R2 v1 2026-06-28T17:04:23.682Z