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The rigidity of Dolbeault-type operators and symplectic circle actions
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.Comment: 8 pages, title changed slightly, final version to be publishe
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