University of Toronto's Symplectic Geometry Seminar

Abstract: Abstract: In this talk we find that the asymptotic nonlinear Maslov index defined on the universal cover of the group of all contact Hamiltonian diffemorphisms of the standard (2n-1)-dimensional contact sphere is a quasimorphism. Then we show our main result: Let M be standard (n-1)-dimensional complex projective space. We prove that the pullback of the asymptotic nonlinear Maslov index to the universal cover of the group of Hamiltonian diffemorphisms of M, when embedded on a diffemorphism supported in a sufficiently small open subset of M, equals -n / 2π vol(M) times the Calabi invariant of the diffemorphism.