29 citations · 50 across the 11 of their papers we have counts for
15 papers
Intersection of Parabolic Subgroups in Euclidean Braid Groups: a short proof
María Cumplido, Federica Gavazzi, Luis Paris
We give a short proof for the fact, already proven by Thomas Haettel, that the arbitrary intersection of parabolic subgroups in Euclidean Braid groups is again a p…
Block mapping class groups and their finiteness properties
Javier Aramayona, Julio Aroca, María Cumplido +2
A Cantor surface is a non-compact surface obtained by gluing copies of a fixed compact surface (a block), with boundary components, in a tree-like fashio…
The Word Problem is Solvable for 3-free Artin groups in Quadratic Time
Rubén Blasco-García, María Cumplido, Rose Morris-Wright
We give a quadratic-time explicit and computable algorithm to solve the word problem for Artin groups that do not contain any relations of length 3. Furthermore, we prove that, giv…
The root extraction problem in braid group-based cryptography
María Cumplido, Delaram Kahrobaei, Marialaura Noce
The root extraction problem in braid groups is the following: given a braid and a number , find such that . In the…
The conjugacy stability problem for parabolic subgroups in Artin groups
María Cumplido
Given an Artin group and a parabolic subgroup , we study if every two elements of that are conjugate in , are also conjugate in . We provide an algorithm to solve…
Parabolic subgroups of large-type Artin groups
María Cumplido, Alexandre Martin, Nicolas Vaskou
We show that the geometric realisation of the poset of proper parabolic subgroups of a large-type Artin group has a systolic geometry. We use this geometry to show that the set of…
A new family of infinitely braided Thompson's groups
Julio Aroca, María Cumplido
We present a generalization of the Dehornoy-Brin braided Thompson group that uses recursive braids. Our new groups are denoted by , for all an…
The root extraction problem for generic braids
María Cumplido, Juan González-Meneses, Marithania Silvero
We show that, generically, finding the -th root of a braid is very fast. More precisely, we provide an algorithm which, given a braid on strands and canonical length …
Parabolic subgroups acting on the additional length graph
Yago Antolín, María Cumplido
Let be an irreducible Artin--Tits group of spherical type. We show that periodic elements of and the elements preserving some parabolic subgroup of …
Commensurability in Artin groups of spherical type
María Cumplido, Luis Paris
Let and be two Artin groups of spherical type, and let (resp. ) be the irreducible components of (resp. ). We show that and $A…
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…
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…
On the minimal positive standardizer of a parabolic subgroup of an Artin-Tits group
María Cumplido
The minimal standardizer of a curve system on a punctured disk is the minimal braid that transforms it into a system formed only by round curves. We give an algorithm to compute it…
On the loxodromic actions of Artin-Tits groups
María Cumplido
Artin-Tits groups act on a certain delta-hyperbolic complex, called the "additional length complex". For an element of the group, acting loxodromically on this complex is a propert…
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…