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.
Authors
- Giuseppe Bargagnati (ORCID: https://orcid.org/0000-0002-9142-6386)
- Pietro Capovilla
- Francesco Milizia (ORCID: https://orcid.org/0000-0001-6738-1053)
- Federica Bertolotti (ORCID: https://orcid.org/0000-0002-6001-9040)
Institutions
- University of Pisa (IT)
- Scuola Normale Superiore (IT)
Publication Details
- Journal
- Geometriae Dedicata
- Published
- 2024-10-14
- DOI
- https://doi.org/10.1007/s10711-024-00939-7
- Primary Topic
- Geometric and Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Scuola Normale Superiore
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni