Circle actions on oriented 4-manifolds

Authors

Donghoon Jang
Oleg R. Musin, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

6-2025

Abstract

In this 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 S1-manifold.

Comments

Original published version available at https://doi.org/10.1142/S1793525325500177

Recommended Citation

Jang, Donghoon, and Oleg R. Musin. 2025. “Circle Actions on Oriented 4-Manifolds.” Journal of Topology and Analysis, 1–28. https://doi.org/10.1142/S1793525325500177.

Publication Title

Journal of Topology and Analysis

DOI

10.1142/S1793525325500177