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

DOI:
https://doi.org/10.1090/S0002-9947-03-03227-6

Published electronically:
July 9, 2003

MathSciNet review:
1990761

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Abstract | References | Similar Articles | Additional Information

Abstract: Assume 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 . 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

Email:
hli@math.uiuc.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03227-6

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