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.
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