Weights of circle actions on oriented manifolds with isolated fixed points
Algebraic Topology
2026-05-05 v1
Abstract
For an action of the circle group 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 -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.
Cite
@article{arxiv.2605.01722,
title = {Weights of circle actions on oriented manifolds with isolated fixed points},
author = {Donghoon Jang},
journal= {arXiv preprint arXiv:2605.01722},
year = {2026}
}