Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Jang, Donghoon
Institution: Pusan National University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Pusan National University
OpenAlex ID: W7160311310