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Weights of circle actions on oriented manifolds with isolated fixed points

  • Donghoon Jang
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Abstract

For an action of the circle group S1 on a compact oriented manifold with isolated fixed points, there is a claim that weights at the fixed points occur in pairs. This phenomenon holds for other types of S1-manifolds, e.g., (almost) complex, symplectic, and unitary manifolds. A known proof of this claim assumes that the isotropy submanifolds are orientable. However, this assumption does not hold in general. In this note, we prove the claim without relying on that assumption.

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Cite

BibTeXRIS
BibTeX
@misc{jang2026weights,
  title = {{Weights of circle actions on oriented manifolds with isolated fixed points}},
  author = {Donghoon Jang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.01722},
  eprint = {2605.01722},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.01722},
}
RIS
TY  - UNPB
TI  - Weights of circle actions on oriented manifolds with isolated fixed points
AU  - Donghoon Jang
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2605.01722
UR  - https://arxiv.org/abs/2605.01722
AB  - For an action of the circle group S^1 on a compact oriented manifold with isolated fixed points, there is a claim that weights at the fixed points occur in pairs. This phenomenon holds for other types of S^1-manifolds, e.g., (almost) complex, symplectic, and unitary manifolds. A known proof of this claim assumes that the isotropy submanifolds are orientable. However, this assumption does not hold in general. In this note, we prove the claim without relying on that assumption.
ER  -