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.
Bargagnati, G., Bertolotti, F., Capovilla, P., Milizia, F. (2024). The action of mapping class groups on de Rham quasimorphisms. GEOMETRIAE DEDICATA, 218(6), 1-21 [10.1007/s10711-024-00939-7].
The action of mapping class groups on de Rham quasimorphisms
Bargagnati, Giuseppe;Capovilla, Pietro;Milizia, Francesco
2024
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.File in questo prodotto:
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