Related papers: The level four braid group

Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants, stable on…

We define and study extensions of Artin's representation and braid monodromy representation to the case of topological and algebraical generalisations of braid groups. In particular we provide faithful representations of braid groups of…

The Burau representation of braid groups and knot Floer homology share a link to the Fox calculus. We make this connection explicit, with the following outcome: if $B$ is the full Burau matrix of any braid, and $A$ is any square submatrix…

Introducing the notion of stabilized fundamental group for the complement of a branch curve in $CP^2$, we define effectively computable invariants of symplectic 4-manifolds that generalize those previously introduced by Moishezon and…

In this paper we give an explicit construction of a symplectic Lefschetz fibration whose total space is a smooth compact four dimensional manifold with a prescribed fundamental group. We also study the numerical properties of the sections…

We describe presentations of braid groups of type ADE and show how these presentations are compatible with mutation of quivers, building on work of Barot and Marsh for Coxeter groups. In types A and D these presentations can be understood…

We establish a braid of interlocking exact sequences containing the group of homotopy self-equivalences of a smooth or topological 4-manifold. The braid is computed for manifolds whose fundamental group is finite of odd order.

We give a topological interpretation of the core group invariant of a surface embedded in S^4. We show that the group is isomorphic to the free product of the fundamental group of the double branch cover of S^4 with the surface as a…

We give a complete classification of homomorphisms from the commutator subgroup of the braid group on $n$ strands to the braid group on $n$ strands when $n$ is at least 7. In particular, we show that each nontrivial homomorphism extends to…

We show that the image of the pure braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of branch points is sufficiently large compared to…

We define braid presentation of edge-oriented spatial graphs as a natural generalization of braid presentation of oriented links. We show that every spatial graph has a braid presentation. For an oriented link it is known that the braid…

\begin{abstract} The reduced Burau representation is a natural action of the braid group $B_n$ on the first homology group $H_1({\tilde{D}}_n;\mathbb{Z})$ of a suitable infinite cyclic covering space ${\tilde{D}}_n$ of the $n$--punctured…

We obtain new presentations for the imprimitive complex reflection groups of type $(de,e,r)$ and their braid groups $B(de,e,r)$ for $d,r \ge 2$. Diagrams for these presentations are proposed. The presentations have much in common with…

The Burau representation enables to define many other representations of the braid group $B_n$ by the topological operation of ``cabling braids''. We show here that these representations split into copies of the Burau representation itself…

The main purpose of this paper is to provide a description of the fundamental group of a symplectic manifold in terms of Floer theoretic objects. As an application, we show that when counted with a suitable notion of multiplicity, non…

The n-strand braid group can be defined as the fundamental group of the configuration space of n unlabeled points in a closed disk based at a configuration where all n points lie in the boundary of the disk. Using this definition, the…

In this paper we calculate fundamental groups (and some of their quotients) of complements of four toric varieties branch curves. For these calculations, we study properties and degenerations of these toric varieties and the braid…

We give a method to produce representations of the braid group $B_n$ of $n-1$ generators ($n\leq \infty$). Moreover, we give sufficient conditions over a non unitary representation for being of this type. This method produces examples of…

We show that the problem of constructing a real rational knot of a reasonably low degree can be reduced to an algebraic problem involving the pure braid group: expressing an associated element of the pure braid group in terms of the…

We propose a family of new representations of the braid groups on surfaces that extend linear representations of the braid groups on a disc such as the Burau representation and the Lawrence-Krammer-Bigelow representation.