Richard D. Wade

activity

20102023

most citedRelative automorphism groups of right-angled Artin groups

12 citations · 50 across the 15 of their papers we have counts for

collaborators

17 papers

math.GT2023

On the geometry of the free factor graph for $Aut (F_{N})$

Mladen Bestvina, Martin R. Bridson, Richard D. Wade

Let $Φ$ be a pseudo-Anosov diffeomorphism of a compact (possibly non-orientable) surface $Σ$ with one boundary component. We show that if $b \in π_{1} (Σ)$ is the boundary word, $ϕ\in…

math.GR2023★ 3 cited

Commensurations of $Aut (F_{N})$ and its Torelli subgroup

Martin R. Bridson, Richard D. Wade

For $N \geq 3$ , the abstract commensurators of both $Aut (F_{N})$ and its Torelli subgroup $IA_{N}$ are isomorphic to $Aut (F_{N})$ itself.

math.GR2022★ 3 cited

Aut-invariant quasimorphisms on groups

Francesco Fournier-Facio, Richard D. Wade

For a large class of groups, we exhibit an infinite-dimensional space of homogeneous quasimorphisms that are invariant under the action of the automorphism group. This class includ…

math.GR2022★ 1 cited

Direct products of free groups in $Aut (F_{N})$

Martin R. Bridson, Richard D. Wade

We give a complete description of the embeddings of direct products of nonabelian free groups into $Aut (F_{N})$ and $Out (F_{N})$ when the number of direct factors is maxi…

math.GR2021★ 1 cited

A note on virtual duality and automorphism groups of right-angled Artin groups

Richard D. Wade, Benjamin Brück

A theorem of Brady and Meier states that a right-angled Artin group is a duality group if and only if the flag complex of the defining graph is Cohen--Macaulay. We use this to give…

math.GR2019

Rigidity of the Torelli subgroup in $O u t (F_{N})$

Sebastian Hensel, Camille Horbez, Richard D. Wade

Let $N$ be at least 4. We prove that every injective homomorphism from the Torelli subgroup into $O u t (F_{N})$ differs from the inclusion by a conjugation in $O u t (F_{N})$ . This applies…

math.GR2019★ 7 cited

Calculating the virtual cohomological dimension of the automorphism group of a RAAG

Matthew B. Day, Andrew W. Sale, Richard D. Wade

We describe an algorithm to find the virtual cohomological dimension of the automorphism group of a right-angled Artin group. The algorithm works in the relative setting; in partic…

math.GR2019★ 1 cited

Commensurations of subgroups of $Out (F_{N})$

Camille Horbez, Richard D. Wade

A theorem of Farb and Handel asserts that for $N \geq 4$ , the natural inclusion from $Out (F_{N})$ into its abstract commensurator is an isomorphism. We give a new proof of the…

math.GR2017★ 12 cited

Relative automorphism groups of right-angled Artin groups

Matthew B. Day, Richard D. Wade

We study the outer automorphism group of a right-angled Artin group $A_{Γ}$ with finite defining graph $Γ$ . We construct a subnormal series for $O u t (A_{Γ})$ such that each consecutive…

math.GR2016★ 1 cited

On the topological dimension of the Gromov boundaries of some hyperbolic $O u t (F_{N})$ -graphs

Mladen Bestvina, Camille Horbez, Richard D. Wade

We give upper bounds, linear in rank, to the topological dimensions of the Gromov boundaries of the intersection graph, the free factor graph and the cyclic splitting graph of a fi…

math.GR2015

Subspace arrangements, BNS invariants, and pure symmetric outer automorphisms of right-angled Artin groups

Matthew B. Day, Richard D. Wade

We introduce a homology theory for subspace arrangements, and use it to extract a new system of numerical invariants from the Bieri-Neumann-Strebel invariant of a group. We use the…

math.GR2014★ 7 cited

Automorphisms of graphs of cyclic splittings of free groups

Camille Horbez, Richard D. Wade

We prove that any isometry of the graph of cyclic splittings of a finitely generated free group $F_{N}$ of rank $N \geq 3$ is induced by an outer automorphism of $F_{N}$ . The same statem…

math.GR2012★ 4 cited

Centralisers of Dehn twist automorphisms of free groups

Moritz Rodenhausen, Richard D. Wade

We refine Cohen and Lustig's description of centralisers of Dehn twists of free groups. We show that the centraliser of a Dehn twist of a free group has a subgroup of finite index…

math.GR2011★ 6 cited

Folding free-group automorphisms

Richard D. Wade

We describe an algorithm that uses Stallings' folding technique to decompose an element of $A u t (F_{n})$ as a product of Whitehead automorphisms (and hence as a product of Nielsen tra…

math.GR2011★ 1 cited

The lower central series of a right-angled Artin group

Richard D. Wade

We give a description of Duchamp and Krob's extension of Magnus' approach to the lower central series of the free group to right-angled Artin groups. We also describe how Lalonde's…

math.GR2011★ 3 cited

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

Richard D. Wade

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 automo…

math.GR2010

Actions of higher-rank lattices on free groups

Martin R. Bridson, Richard D. Wade

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 ge…

On the geometry of the free factor graph for Aut(FN​)

Commensurations of Aut(FN​) and its Torelli subgroup

Aut-invariant quasimorphisms on groups

Direct products of free groups in Aut(FN​)

A note on virtual duality and automorphism groups of right-angled Artin groups

Rigidity of the Torelli subgroup in Out(FN​)

Calculating the virtual cohomological dimension of the automorphism group of a RAAG

Commensurations of subgroups of Out(FN​)

Relative automorphism groups of right-angled Artin groups

On the topological dimension of the Gromov boundaries of some hyperbolic Out(FN​)-graphs

Subspace arrangements, BNS invariants, and pure symmetric outer automorphisms of right-angled Artin groups

Automorphisms of graphs of cyclic splittings of free groups

Centralisers of Dehn twist automorphisms of free groups

Folding free-group automorphisms

The lower central series of a right-angled Artin group

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

Actions of higher-rank lattices on free groups

On the geometry of the free factor graph for $Aut (F_{N})$

Commensurations of $Aut (F_{N})$ and its Torelli subgroup

Direct products of free groups in $Aut (F_{N})$

Rigidity of the Torelli subgroup in $O u t (F_{N})$

Commensurations of subgroups of $Out (F_{N})$

On the topological dimension of the Gromov boundaries of some hyperbolic $O u t (F_{N})$ -graphs