Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Esfahani, Saman Habibi, Li, Yang
Institutions: Duke University, University of Cambridge
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: University of Cambridge
OpenAlex ID: W4403344817