Related papers: Bi-orderings on pure braided Thompson's groups
The braided Thompson group $\mathcal B$ is an asymptotic mapping class group of a sphere punctured along the standard Cantor set, endowed with a rigid structure. Inspired from the case of finite type surfaces we consider a Hatcher-Thurston…
In this paper we will present the results of Artin--Markov on braid groups by using the Groebner--Shirshov basis. As a consequence we can reobtain the normal form of Artin--Markov--Ivanovsky as an easy corollary.
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.
We linearize the Artin representation of the braid group given by (right) automorphisms of a free group providing a linear faithful representation of the braid group. This result is generalized to obtain linear representations for the…
We prove Farber's conjecture on the stable topological complexity of configuration spaces of graphs. The conjecture follows from a general lower bound derived from recent insights into the topological complexity of aspherical spaces. Our…
The central object studied in this paper is a multiplier bimonoid in a braided monoidal category C. Adapting the philosophy of Janssen and Vercruysse, and making some mild assumptions on the category C, we consider a category M whose…
Birman, Ko and Lee have introduced a new monoid ${\cal B}^{*}_{n}$--with an explicit presentation--whose group of fractions is the $n$-strand braid group ${\cal B}_{n}$. Building on a new approach by Digne, Michel and himself, Bessis has…
The main result of this article is that pure orbifold braid groups fit into an exact sequence $1\rightarrow…
A braided generalization of the concept of Hopf algebra (quantum group) is presented. The generalization overcomes an inherent geometrical inhomogeneity of quantum groups, in the sense of allowing completely pointless objects. All…
We observe that Clay-Rolfsen's obstruction of bi-orderability, which uses the classical Alexander polynomial, is not strengthened by using the twisted Alexander polynomials for finite representations unlike many known applications of the…
A $(v,k,\lambda)$-BIBD $(X,\mathcal B)$ can be nested if there is a mapping $\phi:\mathcal B\rightarrow X$ such that $(X,\{B\cup\{\phi(B)\}\mid B\in\mathcal B\})$ is a $(v,k+1,\lambda+1)$-packing. A $(v,k,\lambda)$-BIBD has a (perfect)…
A generalized torsion in a group, an non-trivial element such that some products of its conjugates is the identity. This is an obstruction for a group being bi-orderable. Though it is known that there is a non bi-orderable group without…
We propose two definitions of configuration Lie groupoids and in both the cases we prove a Fadell-Neuwirth type fibration theorem for a class of Lie groupoids. We show that this is the best possible extension, in the sense that, for the…
This note serves as a short and reader-friendly introduction to twisted Brin-Thompson groups, which were recently constructed by Belk and the author to provide a family of simple groups with a variety of interesting properties. Most…
Let n be greater than or equal to 3. We prove that the quaternion group of order 8 is realised as a subgroup of the sphere braid group B\_n(S^2) if and only if n is even. If n is divisible by 4 then the commutator subgroup of B\_n(S^2)…
We prove that the Brin-Thompson groups sV, also called higher dimensional Thompson's groups, are of type F_\infty for all natural numbers s. This result was previously shown for s up to 3, by considering the action of sV on a naturally…
An Ore forest-skein category provides three forest-skein groups equipped with a powerful diagrammatic calculus analogous to Richard Thompson's groups F,T,V. We investigate when forest-skein groups have simple derived subgroups and establish…
We show that the baker's map is a product of transpositions (particularly pleasant involutions), and conclude from this that an existing very short proof of the simplicity of Thompson's group V applies with equal brevity to the higher…
We compare two crossed homomorphisms on a braid group, one defined diagrammatically and the other defined algebraically. We show that these crossed homomorphisms are essentially the same, and compute them in detail for simple braids, namely…
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…