Title:
Moment maps, almost complex structures and quasimorphisms
Abstract:
Given any symplectic manifold of finite volume, we use the action of its
Hamiltonian group on the space of compatible almost complex structures to
construct a non-trivial quasimorphism (on the universal cover of the group).
As an application we show that two norms on \tilde{Ham} are unbounded. Key
notions in the construction include Weinstein's Action homomorphism, the
Donaldson-Fujiki moment map and bounded cocycles given by integration over
geodesic triangles.