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International Journal of Mathematics and Mathematical Sciences
Volume 22, Issue 4, Pages 689-704
http://dx.doi.org/10.1155/S0161171299226890

Reidemeister torsion and integrable Hamiltonian systems

1Institut für Mathematik, E.-M.-Arndt-Universität Greifswald, Jahn-strasse 15a, Greifswald D-17489, Germany
2Instituto de Mathematicas, Universidad Nacional Autonoma de Mexico, Ciudad Universitaria, D. F., Mexico C. P. 04510, Mexico

Received 7 December 1998

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we compute the Reidemeister torsion of an isoenergetic surface for the integrable Hamiltonian system on the 4-dimensional symplectic manifold. We use the spectral sequence defined by the filtration and following Floer-Witten ideas we bring into play the orbits connecting the critical submanifolds.