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arXiv · 1805.00366

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

Antonius Hase
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Abstract

We study the $\mathrm{Out}(F_n)$-action on the second bounded cohomology $H^2_b(F_n, \mathbb{R})$, 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 Mikl\'{o}s Ab\'{e}rt. 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 $g$.

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Antonius Hase. 2018-05-01. Dynamics of $\mathrm{Out}(F_n)$ on the second bounded cohomology of $F_n$. https://arxiv.org/abs/1805.00366

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