Year: 2011
Type: article
Abstract: This paper contains several results concerning circle action on almost complex and smooth manifolds.More precisely, we show that, for an almost-complex manifold M 2mn (resp.a smooth manifold N 4mn ), if there exists a partition) is nonzero, then any circle action on M 2mn (resp.N 4mn ) has at least n + 1 fixed points.When an even-dimensional smooth manifold N 2n admits a semi-free action with isolated fixed points, we show that N 2n bounds, which generalizes a well-known fact in the free case.We also provide a topological obstruction, in terms of the first Chern class, to the existence of semi-free circle action with nonempty isolated fixed points on almost-complex manifolds.The main ingredients of our proofs are Bott's residue formula and rigidity theorem.Recently, Pelayo and Tolman showed that ([19], Theorem 1), if a symplectic manifold (M 2n , ω) has a symplectic S 1 -action and the weights induced from the isotropy
Source: Mathematical Research Letters
Authors: Ping Li, Kefeng Liu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2163661055