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arXiv · 2307.04576

Circle actions on oriented 4-manifolds

Donghoon Jang·Oleg R. Musin
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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 $S^1$-manifold.

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Donghoon Jang, Oleg R. Musin. 2023-07-10. Circle actions on oriented 4-manifolds. https://doi.org/10.1142/s1793525325500177

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