Related papers: Densely ordered braid subgroups

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…

We prove that if a right-angled Artin group $A_\Gamma$ is abstractly commensurable to a group splitting non-trivially as an amalgam or HNN-extension over $\mathbb{Z}^n$, then $A_\Gamma$ must itself split non-trivially over $\mathbb{Z}^k$…

We inspect the normal subgroup structure of the braided Thompson groups Vbr and Fbr. We prove that every proper normal subgroup of Vbr lies in the kernel of the natural quotient Vbr \onto V, and we exhibit some families of interesting such…

For pseudo-Anosov mapping tori with co-orientable invariant foliations and monodromies reversing their co-orientations, a family of taut foliations was constructed in previous work on Dehn fillings with all rational slopes outside a…

Combining the results by Birman and Goldberg, it was proved the normal closure of the pure braid group of the disk $P_n(D)$ in the pure braid group of the torus $P_n(T)$ is the commutator subgroup $[P_n(T),P_n(T)]$. In this paper we are…

We show that any exceptional non-trivial Dehn surgery on a twist knot, except the trefoil, yields a 3-manifold whose fundamental group is left-orderable. This is a generalization of a result of Clay, Lidman and Watson, and also gives a new…

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…

We produce a simple group $G$ of cardinality $\aleph_1$ which is Artinian (every strictly descending chain of subgroups is finite), satisfies a Burnside law and such that for each uncountable subset $Y \subseteq G$ there exists a natural…

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.

For any hyperbolic genus one 2-bridge knot in the 3-sphere, we show that the resulting manifold by $r$-surgery on the knot has left-orderable fundamental group if the slope $r$ lies in some range which depends on the knot.

The aim of this paper is to introduce and study the class of all left braces in which every subbrace is an ideal. We call them Dedekind left braces. It is proved that every finite Dedekind left brace is centrally nilpotent. Structural…

We classify the Artin groups that admit retractions onto all of their parabolic subgroups. Our approach relies on a detailed analysis of triangular subgroups, with a key ingredient being the classification of homomorphisms between dihedral…

In Chapter 1 we give the basic background and notations. We also give a new characterization of the Conrad property for orderings. In Chapter 2, we use the new characterization of the Conradian property to give a classification of groups…

Defined on Birman-Ko-Lee monoids, the rotating normal form has strong connections with the Dehornoy's braid ordering. It can be seen as a process for selecting between all the representative words of a Birman-Ko-Lee braid a particular one,…

A generalization of the topological fundamental group is developed in order to exhibit a topologically complete braid group containing Artin's braid group on infinitely many strands with respect to the following notion of convergence: A…

The space of unordered configurations of distinct points in the plane is aspherical, with Artin's braid group as its fundamental group. Remarkably enough, the space of ordered configurations of distinct points on the real projective line,…

In a previous work [11], the author considered a representation of the braid group \rho: B_n\to GL_m(\Bbb Z[q^{\pm 1},t^{\pm 1}]) (m=n(n-1)/2), and proved it to be faithful for n=4. Bigelow [3] then proved the same representation to be…

Every nontrivial action of the braid group $B_n$ on $\mathbb{R}$ by orientation-preserving homeomorphisms yields, up to conjugation by a homeomorphism of $\mathbb{R}$, a representation $\rho : B_n \rightarrow…

We show that for each positive integer $k$ there exist right-angled Artin groups containing free-by-cyclic subgroups whose monodromy automorphisms grow as $n^k$. As a consequence we produce examples of right-angled Artin groups containing…

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…