Related papers: Infinitary braid groups
We define an action of Artin's braid group on a finite dimensional algebra.
Similar to a tree grammar, a Horn theory can be used to describe an infinite set of terms. In this paper, we present a class of Horn theories such that the set of definable predicates is closed wrt. conjunction and such that the…
A Gauss diagram is a simple, combinatorial way to present a link. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting subdiagrams of certain combinatorial types. In this paper we…
In this paper we introduce the framed pure braid group on $n$ strands of an oriented surface, a topological generalisation of the pure braid group $P_n$. We give different equivalents definitions for framed pure braid groups and we study…
We introduce a finiteness property for braided fusion categories, describe a conjecture that would characterize categories possessing this, and verify the conjecture in a number of important cases. In particular we say a category has F if…
A result of Allock [1](arXiv:math/9907194) states that certain orbifold braid groups contain Artin groups of type $D_n$, $\tilde{B}_n$ and $\tilde{D}_n$ as finite index subgroups. The underlying orbifolds have at most two cone points of…
We classify finite-dimensional complex pointed Hopf algebra with group of group-like elements isomorphic to A_5. We show that any pointed Hopf algebra with infinitesimal braiding associated with the conjugacy class of $\pi$ \in $A_n$ is…
The directions of an infinite graph $G$ are a tangle-like description of its ends: they are choice functions that choose compatibly for all finite vertex sets $X\subseteq V(G)$ a component of $G-X$. Although every direction is induced by a…
Braids can be represented geometrically as curve diagrams. The geometric complexity of a braid is the minimal complexity of a curve diagram representing it. We introduce and study the corresponding notion of geometric generating function.…
We study a subset of square free positive braids and we give a few algebraic characterizations of them and one geometric characterization: the set of positive braids whose closures are unlinks. We describe canonical forms of these braids…
A special class of braids, called woven, is introduced and it is shown that every conjugation class of the braid group contains woven braids. In consequence, links can be presented as plats or closures of woven braids. Restricting on knots,…
Many natural counting problems arise in connection with the normal form of braids--and seem to have never been considered so far. Here we solve some of them by analysing the normality condition in terms of the associated permutations, their…
Many infinite-dimensional Lie groups of interest can be expressed as a union of an ascending sequence of (finite- or infinite-dimensional) Lie groups. In this survey article, we compile general results concerning such ascending unions,…
We study and give examples of braided groupoids, and, a fortiori, non-degenerate solutions of the quiver-theoretical braid equation.
We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the (free) fundamental…
An upper bound of composition series of groups of finite order is obtained. The bound is a nontrivial bound and so far best possible.
If Gamma is any finite graph, then the unlabelled configuration space of n points on Gamma, denoted UC^n(Gamma), is the space of n-element subsets of Gamma. The braid group of Gamma on n strands is the fundamental group of UC^n(Gamma). We…
We construct first examples of infinite groups having property (T) whose Kazhdan constants admit a lower bound independent of the choice of a finite generating set.
We give formulae for the first homology of the $n$-braid group and the pure 2-braid group over a finite graph in terms of graph theoretic invariants. As immediate consequences, a graph is planar if and only if the first homology of the…
We completely describe the structure of the connected components of transversals to a collection of n line segments in R^3. We show that n>2 arbitrary line segments in R^3 admit 0, 1, ..., n or infinitely many line transversals. In the…