12 citations · 27 across the 11 of their papers we have counts for
12 papers
An introduction to the geometric and combinatorial group theory of Artin groups
Rachael Boyd
We give a brief introduction to the geometric and combinatorial group theory of Artin groups. In particular we introduce the conjecture for Artin groups and survey known r…
Even Temperley-Lieb algebras and the dga of planar loops
Rachael Boyd, Guy Boyde, Oscar Randal-Williams +1
We show that the homology of a Temperley-Lieb algebra on an even number of strands has a rich algebraic structure and is highly nontrivial in general. This is achieved by proving t…
The Artin monoid Cayley graph
Rachael Boyd, Ruth Charney, Rose Morris-Wright +1
In this paper we investigate properties of the Artin monoid Cayley graph. This is the Cayley graph of an Artin group with respect to the (infinite) generating set given by th…
The homology of the partition algebras
Rachael Boyd, Richard Hepworth, Peter Patzt
We show that the homology of the partition algebras, interpreted as appropriate Tor-groups, is isomorphic to that of the symmetric groups in a range of degrees that increases with…
Embedding spaces of split links
Rachael Boyd, Corey Bregman
We study the homotopy type of the space of unparametrised embeddings of a split link in . Our main result is a simple descripti…
The minimal genus problem for right angled Artin groups
Rachael Boyd, Thorben Kastenholz, Jean Pierre Mutanguha
We investigate the minimal genus problem for the second homology of a right angled Artin group (RAAG). Firstly, we present a lower bound for the minimal genus of a second homology…
The homology of the Brauer algebras
Rachael Boyd, Richard Hepworth, Peter Patzt
This paper investigates the homology of the Brauer algebras, interpreted as appropriate Tor-groups, and shows that it is closely related to the homology of the symmetric group. Our…
A Deligne complex for Artin Monoids
Rachael Boyd, Ruth Charney, Rose Morris-Wright
In this paper we introduce and study some geometric objects associated to Artin monoids. The Deligne complex for an Artin group is a cube complex that was introduced by the second…
Combinatorics of injective words for Temperley-Lieb algebras
Rachael Boyd, Richard Hepworth
This paper studies combinatorial properties of the 'complex of planar injective words', a chain complex of modules over the Temperley-Lieb algebra that arose in our work on homolog…
The homology of the Temperley-Lieb algebras
Rachael Boyd, Richard Hepworth
This paper studies the homology and cohomology of the Temperley-Lieb algebra TL_n(a), interpreted as appropriate Tor and Ext groups. Our main result applies under the common assump…
The low-dimensional homology of finite-rank Coxeter groups
Rachael Boyd
We give formulas for the second and third integral homology of an arbitrary finitely generated Coxeter group, solely in terms of the corresponding Coxeter diagram. The first of the…
Homological stability for Artin monoids
Rachael Boyd
We prove that certain sequences of Artin monoids containing the braid monoid as a submonoid satisfy homological stability. When the conjecture holds for the associated fam…