Related papers: Braid groups are almost co-Hopfian
The space of configurations of n ordered points in the plane serves as a classifying space for the pure braid group PB_n. Elements of Thompson's group F admit a model similar to braids, except instead of braiding the strands split and…
Braid groups may be defined for every Coxeter diagram. Artin's braid group is of type A. Analogs of Temperley-Lieb, Hecke and Birman-Wenzl algebras exist for B-type. Our general hypothethis is that the braid group of B-type replaces Artin's…
This paper upbuilds the theoretical framework of orbit braids in $M\times I$ by making use of the orbit configuration space $F_G(M,n)$, which enriches the theory of ordinary braids, where $M$ is a connected topological manifold of dimension…
Recently, Cochran and Harvey defined torsion-free derived series of groups and proved an injectivity theorem on the associated torsion-free quotients. We show that there is a universal construction which extends such an injectivity theorem…
We study global injectivity of proper branched coverings defined on the Euclidean $n$-ball in the case when the branch set is compact. In particular we show that such mappings are homeomorphisms when $n=3$ or when the branch set is empty.…
A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…
We consider surgery moves along (n+1)-component Brunnian links in compact connected oriented 3-manifolds, where the framing of the each component is 1/k for k in Z. We show that no finite type invariant of degree < 2n-2 can detect such a…
If G is a finite graph and n is a natural number, then the n-strand braid group of G is the fundamental group of the configuration space of n points on G. This article gives a complete computation of the integral cohomology rings of the…
In this paper we study the homeomorphisms of the disk that are liftable with respect to a simple branched covering. Since any such homeomorphism maps the branch set of the covering onto itself and liftability is invariant up to isotopy…
In this note we show that any homomorphism from a pure surface braid group to a torsion-free hyperbolic group either has a cyclic image or factors through a forgetful map. This extends and gives a new proof of an earlier result of the…
We classify finite pointed braided tensor categories admitting a fiber functor in terms of bilinear forms on symmetric Yetter-Drinfeld modules over abelian groups. We describe the groupoid formed by braided equivalences of such categories…
In this paper, we generalize the tools that were introduced in [Dar19b] in order to study the Andreadakis problem for subgroups of IAn. In particular, we study the behaviour of the Andreadakis problem when we add inner automorphisms to a…
We describe the fundamental group and second homotopy group of ordered $k-$point sets in $Gr(k,n)$ generating a subspace of fixed dimension.
The cohomology of the configuration space of n points in R^3 admits a symmetric group action and has been shown to be isomorphic to the regular representation. One way to prove this is by defining an S^1-action whose fixed point set is the…
Let $H$ be a quasitriangular quasi-Hopf algebra, we construct a braided group $\underline{H}$ in the quasiassociative category of left $H$-modules. Conversely, given any braided group $B$ in this category, we construct a quasi-Hopf algebra…
If $R$ is a ring with 1, we call a unital left $R$-module $M$ co-Hopfian (Hopfian) in the category of left $R$-modules if any monic (epic) endomorphism of $M$ is an automorphism. For commutative Noetherian $R$ we use results of Matlis to…
We consider two natural embeddings between Artin groups: the group G_{tilde{A}_{n-1}} of type tilde{A}_{n-1} embeds into the group G_{B_n} of type B_n; G_{B_n} in turn embeds into the classical braid group Br_{n+1}:=G_{A_n} of type A_n. The…
In this paper we show that the singular braid monoid of an orientable surface can be embedded in a group. The proof is purely topological, making no use of the monoid presentation.
We study ideals in Hall algebras of monoid representations on pointed sets corresponding to certain conditions on the representations. These conditions include the property that the monoid act via partial permutations, that the…
We use braided groups to introduce a theory of $*$-structures on general inhomogeneous quantum groups, which we formulate as {\em quasi-$*$} Hopf algebras. This allows the construction of the tensor product of unitary representations up to…