Fueter sections and $\mathbb{Z}_2$-harmonic 1-forms
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929533541679104 |
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| author | Esfahani, Saman Habibi Li, Yang |
| author_facet | Esfahani, Saman Habibi Li, Yang |
| contents | Motivated by a conjecture of Donaldson and Segal on the counts of monopoles and special Lagrangians in Calabi-Yau 3-folds, we prove a compactness theorem for Fueter sections of charge 2 monopole bundles over 3-manifolds: Let $u_k$ be a sequence of Fueter sections of the charge 2 monopole bundle over a closed oriented Riemannian 3-manifold $(M,g)$, with $L^\infty$-norm diverging to infinity. Then a renormalized sequence derived from $u_k$ subsequentially converges to a non-zero $\mathbb{Z}_2$-harmonic 1-form $\mathcal{V}$ on $M$ in the $W^{1,2}$-topology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_06367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fueter sections and $\mathbb{Z}_2$-harmonic 1-forms Esfahani, Saman Habibi Li, Yang Differential Geometry Analysis of PDEs Geometric Topology Symplectic Geometry Motivated by a conjecture of Donaldson and Segal on the counts of monopoles and special Lagrangians in Calabi-Yau 3-folds, we prove a compactness theorem for Fueter sections of charge 2 monopole bundles over 3-manifolds: Let $u_k$ be a sequence of Fueter sections of the charge 2 monopole bundle over a closed oriented Riemannian 3-manifold $(M,g)$, with $L^\infty$-norm diverging to infinity. Then a renormalized sequence derived from $u_k$ subsequentially converges to a non-zero $\mathbb{Z}_2$-harmonic 1-form $\mathcal{V}$ on $M$ in the $W^{1,2}$-topology. |
| title | Fueter sections and $\mathbb{Z}_2$-harmonic 1-forms |
| topic | Differential Geometry Analysis of PDEs Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2410.06367 |