Zobrazeno 1 - 10
of 56
pro vyhledávání: '"Wade, Richard D."'
Autor:
Petersen, Dan, Wade, Richard D.
We show that the mapping class group of a handlebody is a virtual duality group, in the sense of Bieri and Eckmann. In positive genus we give a description of the dualising module of any torsion-free, finite-index subgroup of the handlebody mapping c
Externí odkaz:
http://arxiv.org/abs/2405.15515
Autor:
Wade, Richard D., Wasserman, Thomas A.
We explain how Cohen--Macaulay classifying spaces are ubiquitous among discrete groups that satisfy Bieri--Eckmann duality, and compare Bieri--Eckmann duality to duality results for Cohen--Macaulay complexes. We use this comparison to give a descript
Externí odkaz:
http://arxiv.org/abs/2405.05881
Autor:
Wade, Richard D., Wasserman, Thomas A.
We prove a duality theorem for Cohen--Macaulay simplicial complexes. This is a generalisation of Poincar\'e Duality, framed in the language of combinatorial sheaves. Our treatment is self-contained and accessible for readers with a working knowledge
Externí odkaz:
http://arxiv.org/abs/2405.05873
Let $\Phi$ be a pseudo-Anosov diffeomorphism of a compact (possibly non-orientable) surface $\Sigma$ with one boundary component. We show that if $b \in \pi_1(\Sigma)$ is the boundary word, $\phi \in {\rm{Aut}}(\pi_1(\Sigma))$ is a representative of
Externí odkaz:
http://arxiv.org/abs/2312.03535
Autor:
Bridson, Martin R., Wade, Richard D.
Publikováno v:
Geom. Funct. Anal. (2024)
For $N \geq 3$, the abstract commensurators of both ${{\rm{Aut}}}(F_N)$ and its Torelli subgroup ${{\rm{IA}}}_N$ are isomorphic to ${{\rm{Aut}}}(F_N)$ itself.
Comment: 30 pages, 5 figures. Version accepted to appear in GAFA
Comment: 30 pages, 5 figures. Version accepted to appear in GAFA
Externí odkaz:
http://arxiv.org/abs/2306.13437
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 includes non-elementary hyperbolic groups, infinitely-ended finitely generat
Externí odkaz:
http://arxiv.org/abs/2211.00800
Autor:
Bridson, Martin R., Wade, Richard D.
We give a complete description of the embeddings of direct products of nonabelian free groups into ${{\rm{Aut}}}(F_N)$ and ${{\rm{Out}}}(F_N)$ when the number of direct factors is maximal. To achieve this, we prove that the image of each such embeddi
Externí odkaz:
http://arxiv.org/abs/2209.01123
Autor:
Wade, Richard D., Brück, Benjamin
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 an example of a RAAG with the property that its outer automorphism gr
Externí odkaz:
http://arxiv.org/abs/2101.08225
Let $N$ be at least 4. We prove that every injective homomorphism from the Torelli subgroup into $Out(F_N)$ differs from the inclusion by a conjugation in $Out(F_N)$. This applies more generally to the following subgroups: every finite-index subgroup
Externí odkaz:
http://arxiv.org/abs/1910.10189
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 particular it also applies to untwisted automorphism groups and basis-conjug
Externí odkaz:
http://arxiv.org/abs/1909.03086