Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Relative flux homomorphism in symplectic geometry


Author: Yildiray Ozan
Journal: Proc. Amer. Math. Soc. 133 (2005), 1223-1230
MSC (2000): Primary 53D22, 53D12; Secondary 53D20
DOI: https://doi.org/10.1090/S0002-9939-04-07611-7
Published electronically: October 15, 2004
MathSciNet review: 2117225
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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 $S^1$ 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53D22, 53D12, 53D20

Retrieve articles in all journals with MSC (2000): 53D22, 53D12, 53D20


Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-04-07611-7
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
Published electronically: October 15, 2004
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2004 American Mathematical Society

American Mathematical Society