Related papers: The BNS-invariant for the pure braid groups

We compute and explicitly describe the Bieri-Neumann-Strebel invariants $\Sigma^1$ for the full and pure braid groups of the sphere $\mathbb{S}^2$, the real projective plane $\mathbb{R}P^2$ and specially the torus $\mathbb{T}$ and the Klein…

We compute the BNS-invariant for the pure symmetric automorphism groups of right-angled Artin groups. We use this calculation to show that the pure symmetric automorphism group of a right-angled Artin group is itself not a right-angled…

We inspect the BNSR-invariants $\Sigma^m(P_n)$ of the pure braid groups $P_n$, using Morse theory. The BNS-invariants $\Sigma^1(P_n)$ were previously computed by Koban, McCammond and Meier. We prove that for any $3\le m\le n$, the inclusion…

We compute the Bieri-Neumann-Strebel invariants $\Sigma^1$ for the generalized solvable Baumslag-Solitar groups $\Gamma_n$ and their finite index subgroups. Using $\Sigma^1$, we show that certain finite index subgroups of $\Gamma_n$ cannot…

We investigate the Bieri--Neumann--Strebel--Renz (BNSR) invariants of irreducible uniform lattices. In the case of a direct product of a tree and a Euclidean space we show that vanishing of the BNSR invariants for all finite-index subgroups…

Given a finite simplicial graph ${\cal G}$, the graph group $G{\cal G}$" is the group with generators in one-to-one correspondence with the vertices of ${\cal G}$ and with relations stating two generators commute if their associated…

We describe the BNS invariant of Kaehler groups. As an application we prove that if the fundamental group of a Kaehler manifold is solvable, it is virtually nilpotent.

We introduce a homology theory for subspace arrangements, and use it to extract a new system of numerical invariants from the Bieri-Neumann-Strebel invariant of a group. We use these to characterize when the set of basis conjugating outer…

Finite type invariants (also known as Vassiliev invariants) of pure braids are considered from a group-theoretic point of view. New results include a construction of a universal invariant with integer coefficients based on the Magnus…

In this paper we give a complete description of the Bieri-Neumann-Strebel-Renz invariants of the Lodha-Moore groups. The second author previously computed the first two invariants, and here we show that all the higher invariants coincide…

We give several applications of the Bieri-Neumann-Strebel invariant on K\"ahler groups. Specifically, we provide simpler proof of the Napier-Ramachandran theorem on the HNN extension about K\"ahler groups and show that amenable K\"ahler…

We present a full description of the Bieri-Neumann-Strebel invariant of restricted permutational wreath products of groups. We also give partial results about the 2-dimensional homotopical invariant of such groups. These results may be…

We define invariants of braids rather than invariants of conjugacy classes of braids. For any pure three-braid we give effective upper and lower bounds for these invariants. This is done in terms of a natural syllable decomposition of the…

We consider the braid groups $\mathbf{B}_n(X)$ on finite simplicial complexes $X$, which are generalizations of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between…

We give a 3-page description of the Gassner invariant / representation of braids / pure braids, along with a description and a proof of its unitarity property.

In this note, a new class of representations of the braid groups $B_{N}$ is constructed. It is proved that those representations contain three kinds of irreducible representations: the trivial (identity) one, the Burau one, and an…

Let X be a Riemannian manifold endowed with a co-compact isometric action of an infinite discrete group. We consider L2 spaces of harmonic vector-valued forms on the product manifold X^N, which are invariant with respect to an action of the…

We study the Newton polytopes of determinants of square matrices defined over rings of twisted Laurent polynomials. We prove that such Newton polytopes are single polytopes (rather than formal differences of two polytopes); this result can…

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…

We introduce and study a family of groups $\mathbf{BB}_n$, called the blocked-braid groups, which are quotients of Artin's braid groups $\mathbf{B}_n$, and have the corresponding symmetric groups $\Sigma_n$ as quotients. They are defined by…