On crossed homomorphisms on symplectic mapping class groups

Kasagawa, Ryoji

doi:10.1090/S0002-9947-08-04618-7

On crossed homomorphisms on symplectic mapping class groups
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by Ryoji Kasagawa PDF

Trans. Amer. Math. Soc. 360 (2008), 4815-4839 Request permission

Abstract:

For a symplectic manifold $(M,\omega )$ with a relation $Q$ between Chern classes of it and the cohomology class of the symplectic form $\omega$, we construct a crossed homomorphism $F_Q$ on the symplectomorphism group of $(M,\omega )$ with values in the cohomology group of $M$ and show an application to the symplectic flux group. Moreover we see that $F_Q$ descends to a crossed homomorphism on the symplectic mapping class group of $(M,\omega )$ and show a nontrivial example of it.

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