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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the construction of certain 6-dimensional symplectic manifolds with Hamiltonian circle actions


Author: Hui Li
Journal: Trans. Amer. Math. Soc. 357 (2005), 983-998
MSC (2000): Primary 53D05, 53D20; Secondary 57R17
Published electronically: October 19, 2004
MathSciNet review: 2110428
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Abstract: Let $(M, \omega)$ be a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian $S^1$ action such that the fixed point set consists of isolated points or surfaces. Assume dim $H^2(M)<3$. In an earlier paper, we defined a certain invariant of such spaces which consists of fixed point data and twist type, and we divided the possible values of these invariants into six ``types''. In this paper, we construct such manifolds with these ``types''. As a consequence, we have a precise list of the values of these invariants.


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Additional Information

Hui Li
Affiliation: Department of Mathematics, University of Illinois Urbana-Champaign, Urbana, Illinois 61801
Address at time of publication: Department of Mathematics, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal
Email: hli@math.uiuc.edu, hli@math.ist.utl.pt

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03762-6
PII: S 0002-9947(04)03762-6
Keywords: Symplectic manifold, Hamiltonian $S^1$ action, moment map, symplectic quotient, symplectic submanifolds.
Received by editor(s): May 5, 2003
Published electronically: October 19, 2004
Additional Notes: The author acknowledges the support of the center of Analysis, Geometry, and Dynamical systems in Lisbon, Portugal, where this paper was revised.
Article copyright: © Copyright 2004 American Mathematical Society