Work

The action of mapping class groups on de Rham quasimorphisms

Year: 2024

Type: article

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.

Source: Geometriae Dedicata

DOI: 10.1007/s10711-024-00939-7

Authors: Giuseppe Bargagnati, Federica Bertolotti, Pietro Capovilla, Francesco Milizia

Institutions: University of Pisa, Scuola Normale Superiore

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,890

Funders: Scuola Normale Superiore, Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni