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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
MathSciNet review:
2117225
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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,
 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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