Related papers: Blocked-braid Groups

The mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base points. We prove that the centralizer of any braid can be expressed in terms of semidirect and direct products of mixed…

The Standard Model of particle physics provides very accurate predictions of phenomena occurring at the sub-atomic level, but the reason for the choice of symmetry group and the large number of particles considered elementary, is still…

The main result of this article is that any braided (resp. annular, planar) diagram group $D$ splits as a short exact sequence $1 \to R \to D \to S \to 1$ where $R$ is a subgroup of some right-angled Artin group and $S$ a subgroup of…

We describe the fundamental groups of ordered and unordered $k-$point sets in the n-dimensional complex space $C^n$ generating an affine subspace of fixed dimension.

Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…

The spaces of triangulations of a given manifold have been widely studied. The celebrated theorem of Pachner~\cite{Pachner} says that any two triangulations of a given manifold can be connected by a sequence of bistellar moves, or Pachner…

For every $n\ge 2$, the {\em surface Houghton group} $\mathcal B_n$ is defined as the asymptotically rigid mapping class group of a surface with exactly $n$ ends, all of them non-planar. The groups $\mathcal B_n$ are analogous to, and in…

In this paper we begin the systematic study of group equations with abelian predicates in the main classes of groups where solving equations is possible. We extend the line of work on word equations with length constraints, and more…

We study the finiteness properties of the braided Higman--Thompson group $bV_{d,r}(H)$ with labels in $H\leq B_d$, and $bF_{d,r}(H)$ and $bT_{d,r}(H)$ with labels in $H\leq PB_d$ where $B_d$ is the braid group with $d$ strings and $PB_d$ is…

In this work, we study the relationship between congruence subgroups $B_n[m]$ and $\mathcal{N}_n(\sigma_1^m)$ the normal closure of $\sigma_1^m$, where $\sigma_1$ is the classical generator of $B_n$. We characterize the conditions under…

In this note we solve the twisted conjugacy problem for braid groups, i.e. we propose an algorithm which, given two braids $u,v\in B_n$ and an automorphism $\phi \in Aut (B_n)$, decides whether $v=(\phi (x))^{-1}ux$ for some $x\in B_n$. As…

We introduce classical and non-deterministic finite automata associated with representations of the braid group. After briefly reviewing basic definitions on finite automata, Coxeter's groups and the associated word problem, we turn to the…

The virtual singular braid group arises as a natural common generalization of classical singular braid groups and virtual braid groups. In this paper, we study several algebraic properties of the virtual singular braid group $VSG_n$. We…

We define a metric filtration of the Gordian graph by an infinite family of 1-dense subgraphs. The n-th subgraph of this family is generated by all knots whose fundamental groups surject to a symmetric group with parameter at least n, where…

Several elementary properties of the symmetric group $S_n$ extend in a nice way to the full transformation monoid $M_n$ of all maps of the set $X:=\{1,2,3,\dots,n\}$ into itself. The group $S_n$ turns out to be in some sense the torsion…

We describe pure braided versions of Thompson's group F. These groups, $BF$ and $\hat{BF}$, are subgroups of the braided versions of Thompson's group V, introduced by Brin and Dehornoy. Unlike V, elements of F are order-preserving self-maps…

We prove that the quotients of the group algebra of the braid group introduced by L. Funar in Comm. Math. Phys., 1995, collapses in characteristic distinct from 2. In characteristic 2 we define several quotients of it, which are connected…

We begin by considering faithful matrix representations of elementary abelian groups in prime characteristic. The representations considered are seen to be determined up to change of bases by a single number. Studying this number leads to a…

Artin's representation is an injective homomorphism from the braid group $B_n$ on $n$ strands into $\operatorname{Aut}\mathbb{F}_n$, the automorphism group of the free group $\mathbb{F}_n$ on $n$ generators. The representation induces maps…

In 1947, in the paper "Theory of Braids", Artin raised the question of whether isotopy and homotopy of braids on the disk coincide. Twenty seven years later, Goldsmith answered his question: she proved that in fact the group structures are…