Extended flux maps on surfaces and the contracted Johnson homomorphism
Geometric Topology
2009-09-04 v2 Symplectic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0808.1695,
title = {Extended flux maps on surfaces and the contracted Johnson homomorphism},
author = {Matthew B. Day},
journal= {arXiv preprint arXiv:0808.1695},
year = {2009}
}
Comments
45 pages, 5 figures; major rewrite, some arguments reworked, a theorem statement corrected