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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.16187 |
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Table of Contents:
- We prove that for any nondegenerate $\mathbb{Z}/2$ harmonic $1$-form, there exists a metric perturbation producing a new nondegenerate $\mathbb{Z}/2$ harmonic $1$-form whose ordinary zero set is discrete. As an application, we show that for generic smooth nondegenerate $\mathbb{Z}/2$ harmonic $1$-forms, the leaf spaces are $\mathbb{Z}$-trees. Moreover, we show that if a $3$-dimensional rational homology sphere admits a smooth nondegenerate $\mathbb{Z}/2$-harmonic $1$-form, then there exists another nondegenerate $\mathbb{Z}/2$-harmonic $1$-form whose singular locus has exactly two connected components.