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Circle Actions on Four Dimensional Almost Complex Manifolds With Discrete Fixed Point Sets.
- Source :
-
IMRN: International Mathematics Research Notices . May2024, Vol. 2024 Issue 9, p7614-7639. 26p. - Publication Year :
- 2024
-
Abstract
- We establish a necessary and sufficient condition for pairs of integers to arise as the weights at the fixed points of an effective circle action on a compact almost complex 4-manifold with a discrete fixed point set. As an application, we provide a necessary and sufficient condition for a pair of integers to arise as the Chern numbers of such an action, answering negatively a question by Sabatini whether |$c_{1}^{2}[M] \leq 3 c_{2}[M]$| holds for any such manifold |$M$|. We achieve this by demonstrating that pairs of integers that arise as weights of a circle action also arise as weights of a restriction of a |$\mathbb {T}^{2}$| -action. Furthermore, we discuss applications to circle actions on complex/symplectic 4-manifolds and semi-free circle actions with discrete fixed point sets. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POINT set theory
*COMPLEX manifolds
*CIRCLE
*INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 10737928
- Volume :
- 2024
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- IMRN: International Mathematics Research Notices
- Publication Type :
- Academic Journal
- Accession number :
- 177084757
- Full Text :
- https://doi.org/10.1093/imrn/rnad285