Circle actions on oriented 4-manifolds

Authors

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

Document Type

Article

Publication Date

2023

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 S1-manifold.

Recommended Citation

Jang, Donghoon, and Oleg R. Musin. "Circle actions on oriented 4-manifolds." arXiv preprint arXiv:2307.04576 (2023).