English

Definite four-manifolds with exotic smooth structures

Geometric Topology 2023-10-26 v1 Symplectic Geometry

Abstract

In this paper we study smooth structures on closed oriented 4-manifolds with fundamental group Z_2 and definite intersection form. We construct infinitely many irreducible, smooth, oriented, closed, definite four-manifolds with fundamental group Z_2 and second Betti number 1 and 2. As an application, we prove that when the second Betti number of a definite four-manifold with fundamental group Z_2 is positive and it admits a smooth structure, then it admits infinitely many smooth structures.

Keywords

Cite

@article{arxiv.2310.16156,
  title  = {Definite four-manifolds with exotic smooth structures},
  author = {András I. Stipsicz and Zoltán Szabó},
  journal= {arXiv preprint arXiv:2310.16156},
  year   = {2023}
}

Comments

21 pages, 4 figures

R2 v1 2026-06-28T13:00:46.461Z