Circle actions on almost complex manifolds with isolated fixed points

The author proved that if the circle acts symplectically on a compact, connected symplectic manifold \(M\) with three fixed points, then \(M\) is equivariantly symplectomorphic to some standard action on \(\mathbb{CP}^2\). In this paper, we extend the result to a circle action on an almost complex m...

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Veröffentlicht in:arXiv.org 2022-01
1. Verfasser: Jang, Donghoon
Format: Artikel
Sprache:eng
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Zusammenfassung:The author proved that if the circle acts symplectically on a compact, connected symplectic manifold \(M\) with three fixed points, then \(M\) is equivariantly symplectomorphic to some standard action on \(\mathbb{CP}^2\). In this paper, we extend the result to a circle action on an almost complex manifold; if the circle acts on a compact, connected almost complex manifold \(M\) with exactly three fixed points, then \(\dim M=4\). Moreover, we deal with the cases of one fixed point and two fixed points.
ISSN:2331-8422
DOI:10.48550/arxiv.1510.00952