Circle actions on 6-dimensional oriented manifolds with 4 fixed points

In this paper, we classify the fixed point data (weights and signs at the fixed points), of a circle action on a 6-dimensional compact connected oriented manifold with 4 fixed points. We prove that it agrees with that of an equivariant connected sum along free orbits of rotations on two 6-spheres, o...

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Bibliographic Details
Published in:Journal of fixed point theory and applications 2023-09, Vol.25 (3), Article 68
Main Author: Jang, Donghoon
Format: Article
Language:English
Subjects:
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
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Summary:In this paper, we classify the fixed point data (weights and signs at the fixed points), of a circle action on a 6-dimensional compact connected oriented manifold with 4 fixed points. We prove that it agrees with that of an equivariant connected sum along free orbits of rotations on two 6-spheres, or that of a linear action on C P 3 . The former case includes that of Petrie’s exotic action on C P 3 .
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-023-01070-y