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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2512.03352 |
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| _version_ | 1866912745756033024 |
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| author | Shevchishin, Vsevolod Smirnov, Gleb |
| author_facet | Shevchishin, Vsevolod Smirnov, Gleb |
| contents | Let $X$ be a closed, oriented four-manifold with $b_2^+ \leq 3$, and suppose $X$ contains a collection of pairwise disjoint embedded $(-2)$-spheres. We prove that there is a Riemannian metric on $X$ such that the Poincare dual of each of these spheres is represented by an anti-self-dual harmonic form. This extends our earlier result for $(-1)$-spheres. The main new ingredient is an application of Eliashberg's $h$-principle for overtwisted contact structures, which we use to construct self-dual harmonic forms on four-orbifolds with prescribed local behaviour near the orbifold singular set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03352 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anti-self-dual blowups II Shevchishin, Vsevolod Smirnov, Gleb Differential Geometry Let $X$ be a closed, oriented four-manifold with $b_2^+ \leq 3$, and suppose $X$ contains a collection of pairwise disjoint embedded $(-2)$-spheres. We prove that there is a Riemannian metric on $X$ such that the Poincare dual of each of these spheres is represented by an anti-self-dual harmonic form. This extends our earlier result for $(-1)$-spheres. The main new ingredient is an application of Eliashberg's $h$-principle for overtwisted contact structures, which we use to construct self-dual harmonic forms on four-orbifolds with prescribed local behaviour near the orbifold singular set. |
| title | Anti-self-dual blowups II |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.03352 |