Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

The rigidity of Dolbeault-type operators and symplectic circle actions

Author: Ping Li
Journal: Proc. Amer. Math. Soc. 140 (2012), 1987-1995
MSC (2010): Primary 37B05, 58J20, 32Q60, 37J10
Posted: September 29, 2011
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Abstract: 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 determine 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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