29 citations · 32 across the 6 of their papers we have counts for
8 papers
Generalisations of Hecke algebras from Loop Braid Groups
Celeste Damiani, Paul Martin, Eric C. Rowell
We introduce a generalisation of the ordinary Hecke algebras informed by the loop braid group and the extension of the Burau representation thereto. The ordinary Heck…
On a canonical lift of Artin's representation to loop braid groups
Celeste Damiani, João Faria Martins, Paul Purdon Martin
Each pointed topological space has an associated -module, obtained from action of its first homotopy group on its second homotopy group. For the -ball with a trivial link wit…
On the group of ring motions of an H-trivial link
Celeste Damiani, Seiichi Kamada
In this paper we compute a presentation for the group of ring motions of the split union of a Hopf link with Euclidean components and a Euclidean circle. A key part of this work is…
Towards a version of Markov's theorem for ribbon torus-links in
Celeste Damiani
In classical knot theory, Markov's theorem gives a way of describing all braids with isotopic closures as links in . We present a version of Markov's theorem for exte…
A Markov's theorem for extended welded braids and links
Celeste Damiani
Extended welded links are a generalization of Fenn, Rimányi, and Rourke's welded links. Their braided counterpart are extended welded braids, which are closely related to ribbon br…
A journey through loop braid groups
Celeste Damiani
In this paper we introduce distinct approaches to loop braid groups, a generalisation of braid groups, and unify all the definitions that have appeared so far in literature, with a…