Abstract
We introduce secondary characteristic classes associated with symplectic diffeomorphism groups which recapture Maslov classes associated with the linear symplectic group. Analogously we also introduce secondary characteristic classes associated with Lie group FIO(N) of invertible Fourier integral operators on a manifold N ([2,3, 4] and [18,19]). As an application we find a nontrivial cycle in FIO(S n) as a lift of the geodesic flow of a sphere.
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Dedicated to Professor Hideki Omori on his 60th birthday
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Miyazaki, N. (2001). Remarks on the Characteristic Classes Associated with the Group of Fourier Integral Operators. In: Maeda, Y., Moriyoshi, H., Omori, H., Sternheimer, D., Tate, T., Watamura, S. (eds) Noncommutative Differential Geometry and Its Applications to Physics. Mathematical Physics Studies, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0704-7_9
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DOI: https://doi.org/10.1007/978-94-010-0704-7_9
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