Extended flux maps on surfaces and the contracted Johnson homomorphism [article]

Matthew B. Day
2009 arXiv   pre-print
On a closed symplectic surface Sigma of genus two or more, we give a new construction of an extended flux map (a crossed homomorphism from the symplectomorphism group Symp(Sigma) to the cohomology group H^1(Sigma;R) that extends the flux homomorphism). This construction uses the topology of the Jacobian of the surface and a correction factor related to the Johnson homomorphism. For surfaces of genus three or more, we give another new construction of an extended flux map using hyperbolic geometry.
arXiv:0808.1695v2 fatcat:rttb2zqzlrcynhvszf7hvgpuri