Circle actions on oriented 4-manifolds
Algebraic Topology
2026-04-01 v3 Combinatorics
Geometric Topology
Abstract
In the present paper, we consider an action of the circle group on a compact oriented 4-manifold. We derive the Atiyah-Hirzebruch formula for the manifold, and associate a graph in terms of data on the fixed point set. We show in the case of isolated fixed points that if an abstract graph satisfies the Atiyah-Hirzebruch formula, then there exists a corresponding 4-dimensional oriented -manifold.
Cite
@article{arxiv.2307.04576,
title = {Circle actions on oriented 4-manifolds},
author = {Donghoon Jang and Oleg R. Musin},
journal= {arXiv preprint arXiv:2307.04576},
year = {2026}
}
Comments
Improved results; we can reduce every weight to 1