66 citations · 281 across the 25 of their papers we have counts for
17 papers · 1 filter
Conjugacy invariants and rigidity in Garside groups: a uniformity phenomenon
Matthieu Calvez, Owen Garnier, Juan González-Meneses +1
Consider an element~ of a Garside group which is rigid in the sense of Garside-theory. Let be the set of rigid conjugates of~ -- this is a well-known characteristic s…
Morse elements in Garside groups are strongly contracting
Matthieu Calvez, Bert Wiest
We prove that in the Cayley graph of any braid group modulo its center , equipped with Garside's generating set, the axes of all pseudo-Anosov braids are strongly contr…
Garside groups and geometry
Bert Wiest
This article in memory of Patrick Dehornoy (1952-2019) is an invitation to Garside theory for mainstream geometric group theorists interested in mapping class groups, curve complex…
On parabolic subgroups of Artin-Tits groups of spherical type
María Cumplido, Volker Gebhardt, Juan González-Meneses +1
We show that, in an Artin-Tits group of spherical type, the intersection of two parabolic subgroups is a parabolic subgroup. Moreover, we show that the set of parabolic subgroups f…
A positive proportion of elements of mapping class groups is pseudo-Anosov
María Cumplido, Bert Wiest
In the Cayley graph of the mapping class group of a closed surface, with respect to any generating set, we look at a ball of large radius centered on the identity vertex, and at th…
Acylindrical hyperbolicity and Artin-Tits groups of spherical type
Matthieu Calvez, Bert Wiest
We prove that, for any irreducible Artin-Tits group of spherical type , the quotient of by its center is acylindrically hyperbolic. This is achieved by studying the addition…
Curve complexes and Garside groups
Matthieu Calvez, Bert Wiest
We present a simple construction which associates to every Garside group a metric space, called the additional length complex, on which the group acts. These spaces share important…
On the genericity of loxodromic actions
Bert Wiest
One way of picking a "generic" element of a finitely generated group is to pick a random element with uniform probability in a large ball centered on in the Cayley graph. If th…
A fast solution to the conjugacy problem in the 4-strand braid group
Matthieu Calvez, Bert Wiest
We present an algorithm for solving the conjugacy search problem in the four strand braid group. The computational complexity is cubic with respect to the braid length.
Lawrence-Krammer-Bigelow representations and dual Garside length of braids
Tetsuya Ito, Bert Wiest
We show that the span of the variable in the Lawrence-Krammer-Bigelow representation matrix of a braid is equal to the twice of the dual Garside length of the braid, as was con…
Fast algorithmic Nielsen-Thurston classification of four-strand braids
Matthieu Calvez, Bert Wiest
We give an algorithm which decides the Nielsen-Thurston type of a given four-strand braid. The complexity of our algorithm is quadratic with respect to word length. The proof of it…
Nielsen-Thurston orderings and the space of braid orderings
Andres Navas, Bert Wiest
We study the topological space of left-orderings of the braid group, and its subspace of Nielsen-Thurston orderings. Our main result is that no Nielsen-Thurston ordering is isolate…
The conjugacy problem in right-angled Artin groups and their subgroups
John Crisp, Eddy Godelle, Bert Wiest
We prove that the conjugacy problem in right-angled Artin groups (RAAGs), as well as in a large and natural class of subgroups of RAAGs, can be solved in linear-time. This class of…
Computational explorations in Thompson's group F
Jose Burillo, Sean Cleary, Bert Wiest
We describe the results of some computational explorations in Thompson's group F. We describe experiments to estimate the cogrowth of F with respect to its standard finite generati…
On word reversing in braid groups
Patrick Dehornoy, Bert Wiest
It has been conjectured that in a braid group, or more generally in a Garside group, applying any sequence of monotone equivalences and word reversings can increase the length of a…
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups
John Crisp, Bert Wiest
We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences…
Free group automorphisms, invariant orderings and topological applications
Dale Rolfsen, Bert Wiest
We are concerned with orderable groups and particularly those with orderings invariant not only under multiplication, but also under a given automorphism or family of automorphisms…