44 citations · 196 across the 18 of their papers we have counts for
20 papers
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…
Groups of convex bodies
Richard Hepworth
In this paper we introduce and study a topological abelian group of convex bodies, analogous to the scissors congruence group and McMullen's polytope algebra, with the universal pr…
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…
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…
Homological stability for Iwahori-Hecke algebras
Richard Hepworth
We show that the Iwahori-Hecke algebras H_n of type A_{n-1} satisfy homological stability, where homology is interpreted as an appropriate Tor group. Our result precisely recovers…
Persistent Magnitude
Dejan Govc, Richard Hepworth
In this paper we introduce the persistent magnitude, a new numerical invariant of (sufficiently nice) graded persistence modules. It is a weighted and signed count of the bars of t…
Magnitude cohomology
Richard Hepworth
Magnitude homology was introduced by Hepworth and Willerton in the case of graphs, and was later extended by Leinster and Shulman to metric spaces and enriched categories. Here we…
On the edge of the stable range
Richard Hepworth
We prove a general homological stability theorem for certain families of groups equipped with product maps, followed by two theorems of a new kind that give information about the l…
Categorifying the magnitude of a graph
Richard Hepworth, Simon Willerton
The magnitude of a graph can be thought of as an integer power series associated to a graph; Leinster introduced it using his idea of magnitude of a metric space. Here we introduce…
Homological stability for families of Coxeter groups
Richard Hepworth
We prove that certain families of Coxeter groups and inclusions satisfy homological stability, meaning that in each degree the homology $…
On string topology of classifying spaces
Richard Hepworth, Anssi Lahtinen
Let G be a compact Lie group. By work of Chataur and Menichi, the homology of the space of free loops in the classifying space of G is known to be the value on the circle in a homo…
Configurations spaces and Theta_n
David Ayala, Richard Hepworth
We demonstrate that Joyal's category Theta_n, which is central to numerous definitions of (infinity,n)-categories, naturally encodes the homotopy type of configuration spaces of ma…
Groups, cacti and framed little discs
Richard Hepworth
Let G be a topological group. Then the based loopspace of G is an algebra over the cacti operad, while the double loopspace of the classifying space of G is an algebra over the fra…
String topology for complex projective spaces
Richard A. Hepworth
In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a comp…
String Topology for Lie Groups
Richard A. Hepworth
In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a dire…
Vector Fields and Flows on Differentiable Stacks
Richard A. Hepworth
This paper introduces the notions of vector field and flow on a general differentiable stack. Our main theorem states that the flow of a vector field on a compact proper differenti…
Morse Inequalities for Orbifold Cohomology
Richard A. Hepworth
This paper begins the study of Morse theory for orbifolds, or more precisely for differentiable Deligne-Mumford stacks. The main result is an analogue of the Morse inequalities tha…
The age grading and the Chen-Ruan cup product
Richard A. Hepworth
We prove that the obstruction bundle used to define the cup-product in Chen-Ruan cohomology is determined by the so-called `age grading' or `degree-shifting numbers'. Indeed, the o…
The topology of certain 3-Sasakian 7-manifolds
Richard A. Hepworth
We calculate the integer cohomology ring and stable tangent bundle of a family of compact, 3-Sasakian 7-manifolds constructed by Boyer, Galicki, Mann, and Rees. Previously only the…