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Transactions of the American Mathematical Society

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Semi-free Hamiltonian circle actions on 6-dimensional symplectic manifolds

Author: Hui Li
Journal: Trans. Amer. Math. Soc. 355 (2003), 4543-4568
MSC (2000): Primary 53D05, 53D20; Secondary 55Q05, 57R19
Published electronically: July 9, 2003
MathSciNet review: 1990761
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Abstract: Assume $(M, \omega)$ is a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian circle action, such that the fixed point set consists of isolated points or compact orientable surfaces. We restrict attention to the case $\dim H^2(M)<3$. We give a complete list of the possible manifolds, and determine their equivariant cohomology rings and equivariant Chern classes. Some of these manifolds are classified up to diffeomorphism. We also show the existence for a few cases.

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Additional Information

Hui Li
Affiliation: Department of Mathematics, University of Illinois, Urbana-Champaign, Illinois 61801
Address at time of publication: Departamento de Matematica, Instituto Superior Tecnico, Lisbon, Portugal 1049-001

Keywords: Circle action, symplectic manifold, symplectic reduction, equivariant cohomology, Morse theory
Received by editor(s): April 17, 2002
Received by editor(s) in revised form: September 18, 2002
Published electronically: July 9, 2003
Article copyright: © Copyright 2003 American Mathematical Society