Extended flux maps on surfaces and the contracted Johnson homomorphism

Details Extended flux maps on surfaces and the contracted Johnson homomorphism Extended flux maps on surfaces and the contracted Johnson homomorphism

2008-08-12

arxiv.org/abs/0808.1695v2

Mathematics

Geometric Topology

45 pages, 5 figures; major rewrite, some arguments reworked, a theorem statement corrected

Scientific paper

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.

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