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A Seifert Dichotomy for Z2-Harmonic One-Forms

  • Weifeng Sun
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Abstract

We establish a dichotomy for Z/2-harmonic one-forms on Seifert fibered rational homology three-spheres. For an oriented base with at most three exceptional fibers, we prove nonexistence along any fixed connection-metric family when the fibers are sufficiently collapsed. With at least four exceptional fibers, existing results give existence for every Riemannian metric. We also complete the corresponding classification for nonorientable bases.

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Cite

BibTeXRIS
BibTeX
@misc{sun2026seifert,
  title = {{A Seifert Dichotomy for Z2-Harmonic One-Forms}},
  author = {Weifeng Sun},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11429},
  eprint = {2609.11429},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11429},
}
RIS
TY  - UNPB
TI  - A Seifert Dichotomy for Z2-Harmonic One-Forms
AU  - Weifeng Sun
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11429
UR  - https://arxiv.org/abs/2609.11429
AB  - We establish a dichotomy for Z/2-harmonic one-forms on Seifert fibered rational homology three-spheres. For an oriented base with at most three exceptional fibers, we prove nonexistence along any fixed connection-metric family when the fibers are sufficiently collapsed. With at least four exceptional fibers, existing results give existence for every Riemannian metric. We also complete the corresponding classification for nonorientable bases.
ER  -