The Nonlinear Maslov index and the Calabi homomorphism

Details The Nonlinear Maslov index and the Calabi homomorphism The Nonlinear Maslov index and the Calabi homomorphism

2006-04-08

arxiv.org/abs/math/0604190v2

Comm. Contemp. Math. Volume 9, Issue 6, 2007, p.769-780

Mathematics

Symplectic Geometry

12 pages

Scientific paper

In this paper we find that the asymptotic nonlinear Maslov index defined on the universal cover of the group of all contact Hamiltonian diffeomorphisms of the standard 2n-1 dimensional contact sphere is a quasimorphism. Then we show our main result: Let M be standard n-1 complex projective space. We prove that the value of the pull back of the asymptotic nonlinear Maslov index to the universal cover of the group of Hamiltonian diffeomorphisms of M, restricted to elements supported in sufficiently small open subsets of M, equals the Calabi invariant of these elements up to a multiplication by a constant.

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