Dynamics of $\mathrm{Out}(F_n)$ on the second bounded cohomology of $F_n$

Abstract

We study the $\mathrm{Out}(F_n)$-action on the second bounded cohomology $H_b^2(F_n,\mathbb{R})$, focusing on the countable-dimensional dense invariant subspace given by Brooks quasimorphisms. We show that this subspace has no finite-dimensional invariant subspaces, in particular no fixpoints, partially answering a question of Miklós Abért. To this end we introduce a notion of speed of an element $g\in \mathrm{Out}(F_n)$, which measures the asymptotic growth rate of bounded cohomology classes under repeated application of $g$.

Master thesis at the Technion; abridged version currently under preparation

References in corpus (2)

• Induced quasi-cocycles on groups with hyperbolically embedded subgroups
• Surface subgroups from linear programming

Cited by in corpus (1)

• The action of mapping class groups on de Rham quasimorphisms