Related papers: Morphismes injectifs entre groupes d'Artin-Tits

We construct a two-level weighted TQFT whose structure coefficents are equivariant intersection numbers on moduli spaces of admissible covers. Such a structure is parallel (and strictly related) to the local Gromov-Witten theory of curves…

This paper shows how to construct coherent presentations (presentations by generators, relations and relations among relations) of monoids admitting a right-noetherian Garside family. Thereby, it resolves the question of finding a unifying…

In 2021, Dzhunusov and Zaitseva classified two-dimensional normal affine commutative algebraic monoids. In this work, we extend this classification to noncommutative monoid structures on normal affine surfaces. We prove that two-dimensional…

We generalize to (certain) Artin groups some results previously known for right-angled Artin groups (RAAGs). First, we generalize a result by Droms, B. Servatius, and H. Servatius, and prove that the derived subgroup of an Artin group is…

Following his discovery that finite metric spaces have injective envelopes naturally admitting a polyhedral structure, Isbell, in his pioneering work on injective metric spaces, attempted a characterization of cellular complexes admitting…

It was shown by Ostrik (2003) and Natale (2017) that a collection of twisted group algebras in a pointed fusion category serve as explicit Morita equivalence class representatives of indecomposable, separable algebras in such categories. We…

The \emph{graph of irreducible parabolic subgroups} is a combinatorial object associated to an Artin-Tits group $A$ defined so as to coincide with the curve graph of the $(n+1)$-times punctured disk when $A$ is Artin's braid group on…

The aim of the present work is to systematically study homomorphisms of Hecke and Artin monoids and thus to develop their comprehensive theory. Our original motivation was the striking observation that parabolic projections of Hecke monoids…

We give a criterion of integrality of an one-dimensional formal group law in terms of congruences satisfied by the coefficients of the canonical invariant differential. For an integral formal group law a p-adic analytic formula for the…

We prove the Tits Alternative for groups acting on $2$-dimensional "recurrent" complexes with uniformly bounded cell stabilisers. This class of complexes includes, among others: $2$-dimensional Euclidean buildings, $2$-dimensional systolic…

Among all affine, flat, finitely presented group schemes, we focus on those that are pure, this includes all groups which are extensions of a finite locally free group by a group with connected fibres. We prove that over an arbitrary base…

We show that the outer automorphism groups of graph products of finitely generated abelian groups satisfy the Tits alternative, are residually finite, their so-called Torelli subgroups are finitely generated, and they satisfy a dichotomy…

We define a representation of the Artin groups of type ADE by monodromy of generalized KZ-systems which is shown to be isomorphic to the generalized Krammer representation originally defined by A.M. Cohen and D. Wales, and independantly by…

We prove \cite[Conjecture~5.17]{Clausen} on the local light--profinite structure of smooth $p$-adic analytic Artin stacks. The argument proceeds in several reductions. First, by proving a generalization of van~Dantzig theorem for groupoids,…

We introduce a Grothendieck ring of higher Artin stacks generalizing the Grothendieck ring of algebraic varieties. We show that this ring is not trivial by noticing that it factors the invariant "number of rational points over a finite…

We calculate the higher topological complexity TC$_s$ for the complements of reflection arrangements, in other words for the pure Artin type groups of all finite complex reflection groups. In order to do that we introduce a simple…

A theorem proved by Dobrinskaya in 2006 shows that there is a strong connection between the $K(\pi,1)$ conjecture for Artin groups and the classifying space of Artin monoids. More recently Ozornova obtained a different proof of…

We conjecture that the word problem of Artin-Tits groups can be solved without introducing trivial factors ss^{-1} or s^{-1}s. Here we make this statement precise and explain how it can be seen as a weak form of hyperbolicity. We prove the…

We describe a new approach to the Word Problem for Artin-Tits groups and, more generally, for the enveloping group U(M) of a monoid M in which any two elements admit a greatest common divisor. The method relies on a rewrite system R(M) that…

We study faithful realisations of Coxeter groups over fusion rings and study Vinberg systems associated to them. We show that they induce embeddings of hyperplane complements, which provide geometrical realisations of certain types of…