4 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 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…