Anti-self-dual blowups

2023/08/06 by Vsevolod Shevchishin, Shevchishin, Vsevolod, Gleb Smirnov +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2308.03090

openalex publication_date 2023/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a closed, oriented four-manifold containing an embedded sphere with self-intersection number (-1). Suppose that b₂⁺(X) ≤ 3. We show that there exists a Riemannian metric on X such that the cohomology class dual to this sphere is represented by an anti-self-dual harmonic form. Furthermore, such a metric can be constructed even when there are multiple disjoint embedded (-1)-spheres.

Cited by

• Anti-self-dual blowups II

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