On the construction of certain 6-dimensional symplectic manifolds with Hamiltonian circle actions
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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.References
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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
- 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.
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 983-998
- MSC (2000): Primary 53D05, 53D20; Secondary 57R17
- DOI: https://doi.org/10.1090/S0002-9947-04-03762-6
- MathSciNet review: 2110428