Definite four-manifolds with exotic smooth structures

2023/10/24 by András I. Stipsicz, Zoltán Szabó, Stipsicz, András I. +1 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2310.16156

openalex publication_date 2023/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study smooth structures on closed oriented 4-manifolds with fundamental group Z₂ and definite intersection form. We construct infinitely many irreducible, smooth, oriented, closed, definite four-manifolds with fundamental group Z₂ 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 Z₂ is positive and it admits a smooth structure, then it admits infinitely many smooth structures.

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