Fueter sections and $\mathbb{Z}_2$-harmonic 1-forms

Saman Habibi Esfahani; Yang Li

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arXiv · 2410.06367

Fueter sections and $\mathbb{Z}_2$-harmonic 1-forms

Saman Habibi Esfahani·Yang Li

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Abstract

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.

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BibTeX RIS

Saman Habibi Esfahani, Yang Li. 2024-10-08. Fueter sections and $\mathbb{Z}_2$-harmonic 1-forms. https://arxiv.org/abs/2410.06367

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