Year: 2026
Type: preprint
Abstract: In this paper, we develop methods for constructing $\mathbb{Z}/2$-harmonic 1-forms in dimension three by varying the background metric. On $\mathbb{R}^3$, we construct an example for which the complement of the smooth locus in the singular set is a Cantor set. We realize every finite graph with positive even valence at each vertex as the monodromy locus of a $\mathbb{Z}/2$-harmonic 1-form on $B^3$. We also construct desingularization models for every critical $\mathbb{Z}/2$-eigensection, agreeing exactly with the associated homogeneous model outside a compact set. Finally, we construct a nondegenerate $\mathbb{Z}/2$-harmonic 1-form on every closed connected oriented three-manifold for a suitable smooth metric.
Source: arXiv (Cornell University)
Authors: Chen, Jiahuang, He, Siqi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213500367