The action of mapping class groups on de Rham quasimorphisms

Abstract

We study the action of the mapping class group on the subspace of de Rham classes in the degree-two bounded cohomology of a hyperbolic surface. In particular, we show that the only fixed nontrivial finite-dimensional subspace is the one generated by the Euler class. As a consequence, we get that the action of the mapping class group on the space of de Rham quasimorphisms has no fixed points.

arXiv comment23 pages, 4 figures, revised version according to the referee's comments

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