8 citations · 31 across the 13 of their papers we have counts for
15 papers
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…
Property for some spherical and affine Artin-Tits groups
Matthieu Calvez, Ignat Soroko
Let . In this note we give a short uniform proof of property for the Artin-Tits groups of spherical types , , , (), their pure subg…
Euclidean Artin-Tits groups are acylindrically hyperbolic
Matthieu Calvez
In this paper we show the statement in the title. To any Garside group of finite type, Wiest and the author associated a hyperbolic graph called the \emph{additional length graph}…
Curve graphs for Artin-Tits groups of type , and are hyperbolic
Matthieu Calvez, Bruno A. Cisneros de la Cruz
The \emph{graph of irreducible parabolic subgroups} is a combinatorial object associated to an Artin-Tits group defined so as to coincide with the curve graph of the -ti…
Hyperbolicity of the complex of parabolic subgroups of Artin-Tits groups of type
Matthieu Calvez
We show that the complex of parabolic subgroups associated to the Artin-Tits group of type is hyperbolic
Hyperbolic structures for Artin-Tits groups of spherical type
Matthieu Calvez, Bert Wiest
The goal of this mostly expository paper is to present several candidates for hyperbolic structures on irreducible Artin-Tits groups of spherical type and to elucidate some relatio…
Conjugacy stability of parabolic subgroups of Artin-Tits groups of spherical type
Matthieu Calvez, Bruno Cisneros, María Cumplido
We give a complete classification of conjugacy stable parabolic subgroups of Artin-Tits groups of spherical type. This answers a question posed by Ivan Marin and generalizes a theo…
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…
Garside-theoretic analysis of Burau representations
Matthieu Calvez, Tetsuya Ito
We establish relations between both the classical and the dual Garside structures of the braid group and the Burau representation. Using the classical structure, we formulate a non…
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.
Fast nielsen-thurston classification of braids
Matthieu Calvez
We prove the existence of an algorithm which solves the reducibility problem in braid groups and runs in quadratic time with respect to the braid length for any fixed braid index.
Dual Garside structure and reducibility of braids
Matthieu Calvez
Benardete, Gutierrez and Nitecki showed an important result which relates the geometrical properties of a braid, as a homeomorphism of the punctured disk, to its algebraic Garside-…
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…