Year: 2024
Type: article
Abstract: In this paper, we study smooth structures on closed, oriented four-manifolds with fundamental group Z / 2 Z \mathbb{Z}/2\mathbb{Z} and definite intersection form. We construct infinitely many irreducible, oriented, closed, definite, smooth four-manifolds with π 1 = Z / 2 Z \pi_{1}=\mathbb{Z}/2\mathbb{Z} and b 2 = 1 b_{2}=1 , and b 2 = 2 b_{2}=2 . As an application, we prove that, when the second Betti number b 2 b_{2} of a definite four-manifold with π 1 = Z / 2 Z \pi_{1}=\mathbb{Z}/2\mathbb{Z} is positive and it admits a smooth structure, then it admits infinitely many smooth structures.
Authors: András I. Stipsicz, Zoltán Szabó
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403637086