Related papers: Commutator Subgroups of Singular Braid Groups

Some curious structural similarities between a recent braid- and Hurwitz algebraic description of the unbroken internal symmetries for a single generations of Standard Model fermions were recently identified. The non-trivial braid groups…

This paper is devoted to the proof of a structural theorem, concerning certain homomorphic images of Artin braid group on $n$ strands in finite symmetric groups. It is shown that any one of these permutation groups is an extension of the…

In the present paper the representation of the virtual braid group $VB_n$ into the automorphism group of free product of the free group and free abelian group is constructed. This representation generalizes the previously constructed ones.…

Let n\geq 3. We classify the finite groups which are realised as subgroups of the sphere braid group B_n(S^2). Such groups must be of cohomological period 2 or 4. Depending on the value of n, we show that the following are the maximal…

A generalized numerical semigroup is a submonoid $S$ of $\mathbb{N}^d$ with finite complement in it. We characterize isomorphisms between these monoids in terms of permutation of coordinates. Considering the equivalence relation that…

The braid groups B_n can be defined as the mapping class group of the n-punctured disc. The Lawrence-Krammer representation of the braid group B_n is the induced action on a certain twisted second homology of the space of unordered pairs of…

We prove that, for $n\geq 3$, the minimal dimension of a model of the classifying space of the full braid group $B_n$, and of the pure braid group $P_n$, with respect to the family of virtually cyclic groups is $n$.

We introduce the relative Coxeter groupoid and construct intrinsic relative braid group symmetries for quantum supersymmetric pairs of type sAIII. These symmetries are constructed by establishing new intertwining properties of quasi…

We study the homology of $[P_n,P_n]$, the commutator subgroup of the pure braid group on $n$ strands, and show that $H_l([P_n,P_n])$ contains a free abelian group of infinite rank for all $1\leq l\leq n-2$. As a consequence we determine the…

Let M be a compact, connected non-orientable surface without boundary and of genus g greater than or equal to 3. We investigate the pure braid groups P_n(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact…

We study braided Hochschild and cyclic homology of ribbon algebras in braided monoidal categories, as introduced by Baez and by Akrami and Majid. We compute this invariant for several examples coming from quantum groups and braided groups.

We say that a finitely generated group $\Gamma$ is self-simulable if every effectively closed action of $\Gamma$ on a closed subset of $\{\texttt{0},\texttt{1}\}^{\mathbb{N}}$ is the topological factor of a $\Gamma$-subshift of finite type.…

Let $B_4$ (resp. $PB_4$) be the braid group (resp. the pure braid group) on 4 strands and $NFI_{PB_4}(B_4)$ be the poset whose objects are finite index normal subgroups of $B_4$ that are contained in $PB_4$. In this paper, we introduce…

A new infinite series of rational affine algebraic varieties is constructed whose automorphism group contains the automorphism group ${\rm Aut}(F_n)$ of the free group $F_n$ of rank $n$. The automorphism groups of such varieties are…

In our preceding papers we started considering the categories of tangles with flat G-connections in their complements, where G is a simple complex algebraic group. The braiding (or the commutativity constraint) in such categories satisfies…

We study quasimorphisms and bounded cohomology of a variety of braided versions of Thompson groups. Our first main result is that the Brin--Dehornoy braided Thompson group $bV$ has an infinite-dimensional space of quasimorphisms and thus…

Let $\beta:=\sigma_1\sigma_2^{-1}$ be a braid in $B_3$, where $B_3$ is the braid group on 3 strings and $\sigma_1, \sigma_2$ are the standard Artin generators. We use Gauss diagram formulas to show that for each natural number $n$ not…

In this article we give self-contained existence proofs for the sporadic simple groups Co_2 and Fi_{22} using the second author's algorithm [10] constructing finite simple groups from irreducible subgroups of GL_n(2). These two sporadic…

We consider categories of Soergel bimodules for the symmetric groups S_n in their gl(n)-realizations for all n and assemble them into a locally linear monoidal bicategory. Chain complexes of Soergel bimodules likewise form a locally…

In this paper we introduce distinct approaches to loop braid groups, a generalisation of braid groups, and unify all the definitions that have appeared so far in literature, with a complete proof of the equivalence of these definitions.…