arXiv subjects

Richard D. Wade

Publications and source records attributed to Richard D. Wade.

21 records · Page 2Linked to original sources

arXiv2013

Johnson homomorphisms and actions of higher-rank lattices on right-angled Artin groups

Let G be a real semisimple Lie group with no compact factors and finite centre, and let $Λ$ be a lattice in G. Suppose that there exists a homomorphism from $Λ$ to the outer automorphism group of a right-angled Artin group $A_Γ$ with infinite image. We give an upper bound to the real rank of G that is determined by the structure of cliques in $Γ$. An essential tool is the Andreadakis-Johnson filtration of the Torelli subgroup $\mathcal{T}}(A_Γ)$ of $Aut(A_Γ)$. We answer a question of Day relating to the abelianisation of $\mathcal{T}}(A_Γ)$, and show that $\mathcal{T}}(A_Γ)$ and its image in $Out(A_Γ)$ are residually torsion-free nilpotent.

math.GR↗

arXiv2013

Folding free-group automorphisms

We describe an algorithm that uses Stallings' folding technique to decompose an element of $Aut(F_n)$ as a product of Whitehead automorphisms (and hence as a product of Nielsen transformations.) We use this to give an alternative method of finding a finite generating set for the subgroup of $Aut(F_n)$ that fixes a subset $Y$ of the basis elements, and the subgroup that fixes each element of $Y$ up to conjugacy. We show that the intersection of this latter subgroup with $IA_n$ is also finitely generated.

math.GR↗

arXiv2011

Actions of higher-rank lattices on free groups

If $G$ is a semisimple Lie group of real rank at least 2 and $Γ$ is an irreducible lattice in $G$, then every homomorphism from $Γ$ to the outer automorphism group of a finitely generated free group has finite image.

math.GR↗