Primitive Circle Actions on Almost Complex Manifolds with Isolated Fixed Points
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Let the circle act on a compact almost complex manifold M with a non-empty discrete fixed point set. To each fixed point, there are associated non-zero integers called weights. A positive weight w is called primitive if it cannot be written as the sum of positive weights, other than w itself. In this paper, we show that if every weight is primitive, then the Todd genus Todd(M) of M is positive and there are Todd(M) · 2n fixed points, where dim M = 2n. This generalizes the result for symplectic semi- free actions by Tolman and Weitsman [8], the result for semi-free actions on almost complex manifolds by the author [6], and the result for certain symplectic actions by Godinho [1].
Abstract
Let the circle act on a compact almost complex manifold M with a non-empty discrete fixed point set. To each fixed point, there are associated non-zero integers called weights. A positive weight w is called primitive if it cannot be written as the sum of positive weights, other than w itself. In this paper, we show that if every weight is primitive, then the Todd genus Todd(M) of M is positive and there are Todd(M) · 2n fixed points, where dim M = 2n. This generalizes the result for symplectic semi- free actions by Tolman and Weitsman [8], the result for semi-free actions on almost complex manifolds by the author [6], and the result for certain symplectic actions by Godinho [1].
참고문헌 (8)
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- D. Jang, "Circle actions on almost complex manifolds with isolated fixed points", Journal of Geometry and Physics, 119, pp.187~192 (2017)
- D. Jang, "Circle actions on almost complex manifolds with 4 fixed points", Math. Z (2019)[DOI]
- P. Li, "The rigidity of Dolbeault-type operators and symplectic circle actions", Proc. Amer. Math. Soc, 140, pp.1987~1995 (2012)
- S. Tolman, "On semifree symplectic circle actions with isolated fixed points", Topology, 39(2), pp.299~309 (2000)