Extended flux maps on surfaces and the contracted Johnson homomorphism

2008/08/12 by Matthew B. Day, Day, Matthew B.
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0808.1695

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 H¹(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.

Related

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