The braid monodromy of plane algebraic curves and hyperplane arrangements (original) (raw)

Braid monodromy and topology of plane curves

Duke Mathematical Journal, 2003

In this paper we prove that braid monodromy of an affine plane curve determines the topology of a related projective plane curve. 1 2 E. ARTAL, J. CARMONA, AND J.I. COGOLLUDO

Artin Covers of the Braid Groups

Journal of Knot Theory and Its Ramifications, 2012

Computation of fundamental groups of Galois covers recently led to the construction and analysis of Coxeter covers of the symmetric groups [L. H. Rowen, M. Teicher and U. Vishne, Coxeter covers of the symmetric groups, J. Group Theory8 (2005) 139–169]. In this paper we consider analog covers of Artin's braid groups, and completely describe the induced geometric extensions of the braid group.

Braid monodromy of complex line arrangements

Kodai Mathematical Journal, 1999

Let V be the complex vector space C 7 , s/ an arrangement in V, i.e. a finite family of hyperplanes in V In , Moishezon associated to any algebraic plane curve <# of degree n a braid monodromy homomorphism θ F s -> B(n), where F s is a free group, B(ή) is the Artm braid group. In this paper, we will determine the braid monodromy for the case when # is an arrangement stf of complex lines in C 2 , using the notion of labyrinth of an arrangement. As a corollary we get the braid monodromy presentation for the fundamental group of the complement to the arrangement.

Braid groups in complex projective spaces

Advances in Geometry, 2012

We describe the fundamental groups of ordered and unordered k−point sets in CP n generating a projective subspace of dimension i. We apply these to study connectivity of more complicated configurations of points.

Some monodromy representations of generalized braid groups

Communications in Mathematical Physics, 1994

A flat connection on the trivial bundle over the complement in C" of the complexification of the system of the reflecting hyperplanes of the B n , D n Coxeter groups is built from a simple Lie algebra and its representation. The corresponding monodromy representations of the generalized braid groups XB n , XD n are computed in the simplest case.

Braided surfaces and their characteristic maps

arXiv (Cornell University), 2020

We show that branched coverings of surfaces of large enough genus arise as characteristic maps of braided surfaces, thus being 2-prems. In the reverse direction we show that any nonabelian surface group has infinitely many finite simple nonabelian groups quotients with characteristic kernels which do not contain any simple loops and hence the quotient maps do not factor through free groups. By a pullback construction, finite dimensional Hermitian representations of braid groups provide invariants for the braided surfaces. We show that the strong equivalence classes of braided surfaces are separated by such invariants if and only if they are profinitely separated.

Homotopical presentations of braid groups via reduced lifts

2021

In [De2], Deligne showed that the reduced lift presentation of a finite type generalized braid group remains correct if it is (suitably) interpreted as a presentation of a topological monoid. In this expository paper, we point out that Deligne’s argument does not require the ‘finite type’ hypothesis, so it gives a different proof of [Do, Thm. 5.1]. We also review how to use this result to construct an action of the braid group on the finite or affine Hecke ∞-category via intertwining functors.

On braid groups and right-angled Artin groups

Geometriae Dedicata, 2014

In this article we prove a special case of a conjecture of A. Abrams and R. Ghrist about fundamental groups of certain aspherical spaces. Specifically, we show that the n−point braid group of a linear tree is a right angled Artin group for each n.