Extended flux maps on surfaces and the contracted Johnson homomorphism

Matthew B. Day

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arXiv · 0808.1695

Extended flux maps on surfaces and the contracted Johnson homomorphism

Matthew B. Day

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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.

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Matthew B. Day. 2009-09-03. Extended flux maps on surfaces and the contracted Johnson homomorphism. https://arxiv.org/abs/0808.1695

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