Matthew Day, Caltech

TITLE: Extended flux map on surfaces

ABSTRACT: An extended flux map is a crossed homomorphism on the symplectomorphism group of a symplectic manifold that extends the classical flux homomorphism (defined on the connected component of the identity). I will give three distinct constructions of extended flux maps on a symplectic surface--one using hyperbolic geometry, one using the Jacobian torus of the surface, and an algebraic construction. I will then explain a connection between the differences of these maps and the Johnson homomorphism on the Torelli subgroup of the mapping class group of the surface.