Anti-self-dual blowups
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910694568361984 |
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| author | Shevchishin, Vsevolod Smirnov, Gleb |
| author_facet | Shevchishin, Vsevolod Smirnov, Gleb |
| contents | Let $X$ be a closed, oriented four-manifold containing an embedded sphere with self-intersection number $(-1)$. Suppose that $b_2^+(X) \leq 3$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03090 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Anti-self-dual blowups Shevchishin, Vsevolod Smirnov, Gleb Differential Geometry Let $X$ be a closed, oriented four-manifold containing an embedded sphere with self-intersection number $(-1)$. Suppose that $b_2^+(X) \leq 3$. 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. |
| title | Anti-self-dual blowups |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2308.03090 |