Low dimensional free and linear representations of $\mathrm{Out}(F_3)$

Abstract

We study homomorphisms from $\mathrm{Out}(F_3)$ to $\mathrm{Out}(F_5)$, and $\mathrm{GL}(m,K)$ for $m<7$, where $K$ is a field of characteristic other than 2 or 3. We conclude that all $K$-linear representations of dimension at most 6 of $\mathrm{Out}(F_3)$ factor through $\mathrm{GL}(3,Z)$, and that all homomorphisms from $\mathrm{Out}(F_3)$ to $\mathrm{Out}(F_5)$ have finite image.

Final version

References in corpus (3)

• Cohomological Aspects of Magnus Expansions
• Injections of mapping class groups
• Hochschild-Pirashvili homology on suspensions and representations of $Out(F_n)$

Cited by in corpus (3)

• Hochschild-Pirashvili homology on suspensions and representations of $Out(F_n)$
• Nielsen realisation for untwisted automorphisms of right-angled Artin groups
• Outer actions of $\mathrm{Out}(F_n)$ on small right-angled Artin groups