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Relative flux homomorphism in symplectic geometry

Author(s): Yildiray Ozan
Journal: Proc. Amer. Math. Soc. 133 (2005), 1223-1230.
MSC (2000): Primary 53D22, 53D12; Secondary 53D20
Posted: October 15, 2004
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Abstract: In this work we define a relative version of the flux homomorphism, introduced by Calabi in 1969, for a symplectic manifold. We use it to study (the universal cover of) the group of symplectomorphisms of a symplectic manifold leaving a Lagrangian submanifold invariant. We also show that some quotients of the universal covering of the group of symplectomorphisms are stable under symplectic reduction.

References:

1.: E. Calabi, On the group of automorphisms of a symplectic manifold, Problems in Analysis (ed. R. Gunning), Princeton University Press, New Jersey, 1970. MR 50:3268
2.: P. Griffiths, J. Harris, Principles of Algebraic Geometry, John Wiley $\&$ Sons, Inc., New York, 1994. MR 95d:14001
3.: H. Li, $\pi_1$ of Hamiltonian manifolds, Proc. Amer. Math. Soc. 131 (2003), 3579-3582.MR 2004b:53145
4.: D. McDuff, D. Salamon, Introduction to symplectic topology, Oxford University Press, New York, 1997.
5.: Y. Ozan, On cohomology of invariant submanifolds of Hamiltonian actions, preprint.
6.: -, Homology of non orientable real algebraic varieties, preprint.
7.: -, On homology of real algebraic varieties, Proc. Amer. Math. Soc. 129 (2001), 3167-3175. MR 2002m:14048

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Additional Information:

Yildiray Ozan
Affiliation: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Email: ozan@metu.edu.tr

DOI: 10.1090/S0002-9939-04-07611-7
PII: S 0002-9939(04)07611-7
Keywords: Symplectic manifold, Lagrangian submanifold, symplectomorphism, flux homomorphism
Received by editor(s): October 18, 2003
Received by editor(s) in revised form: December 13, 2003.
Posted: October 15, 2004
Communicated by: Jon G. Wolfson
Copyright of article: Copyright 2004, American Mathematical Society


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