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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: 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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Additional Information

Ping Li
Affiliation: Department of Mathematics, Tongji University, Shanghai 200092, People’s Republic of China
Email: pingli@tongji.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11067-0
PII: S 0002-9939(2011)11067-0
Keywords: Rigidity, Dolbeault-type operator, symplectic circle action, Hamiltonian circle action
Received by editor(s): October 1, 2010
Received by editor(s) in revised form: February 2, 2011
Published electronically: September 29, 2011
Additional Notes: The author’s research is supported by the Natural Science Foundation of China (grant No. 11101308) and the Program for Young Excellent Talents in Tongji University.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2011 American Mathematical Society