Definite four-manifolds with exotic smooth structures

András I. Stipsicz; Zoltán Szabó

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arXiv · 2310.16156

Definite four-manifolds with exotic smooth structures

András I. Stipsicz·Zoltán Szabó

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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.

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BibTeX RIS

András I. Stipsicz, Zoltán Szabó. 2023-10-24. Definite four-manifolds with exotic smooth structures. https://arxiv.org/abs/2310.16156

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