The rigidity of Dolbeault-type operators and symplectic circle actions

Details The rigidity of Dolbeault-type operators and symplectic circle actions The rigidity of Dolbeault-type operators and symplectic circle actions

2010-07-27

arxiv.org/abs/1007.4665v3

Proc. Amer. Math. Soc. 140. (2012), 1987-1995

Mathematics

Symplectic Geometry

8 pages, title changed slightly, final version to be published

Scientific paper

Following the idea of Lusztig, Atiyah-Hirzebruch and Kosniowski, we note that the Dolbeault-type operators on compact, almost-complex manifolds are rigid. When the circle action has isolated fixed points, this rigidity result will produce many identities concerning the weights on the fixed points. In particular, it gives a criterion to detemine whether or not a symplectic circle action with isolated fixed points is Hamiltonian. As applications, we simplify the proofs of some known results related to symplectic circle actions, due to Godinho, Tolman-Weitsman and Pelayo-Tolman, and generalize some of them to more general cases.

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