Hurwitz Stabilisers of Some Short Redundant Artin Systems for the Braid Group Br 3
نویسنده
چکیده
We investigate the Hurwitz action of the braid group Br n on the n-fold Cartesian product Br n 3 and determine some stabilisers of its Artin systems. Our algebraic result is complemented by a geometric study of families of plane polynomial coverings of degree 3. Together they lead to characterisations of the set of paths realised by degenerations of the polynomials as defined by Donaldson [Do].
منابع مشابه
A Dual Braid Monoid for the Free Group
We construct a quasi-Garside monoid structure for the free group. This monoid should be thought of as a dual braid monoid for the free group, generalising the constructions by Birman-Ko-Lee and by the author of new Garside monoids for Artin groups of spherical type. Conjecturally, an analog construction should be available for arbitrary Artin groups and for braid groups of well-generated comple...
متن کاملThe Hurwitz Action and Braid Group Orderings
In connection with the so-called Hurwitz action of homeomorphisms in ramified covers we define a groupoid, which we call a ramification groupoid of the 2sphere, constructed as a certain path groupoid of the universal ramified cover of the 2-sphere with finitely many marked-points. Our approach to ramified covers is based on cosheaf spaces, which are closely related to Fox’s complete spreads. A ...
متن کاملThe homology of the Milnor fiber for classical braid groups
Let (W, S) be a Coxeter system, with W a finite, irreducible Coxeter group and let GW be the associated Artin group (see Bourbaki [5] for an introduction to Coxeter groups and their classifications and Brieskorn and Saito [6] for relations between Coxeter groups and Artin groups ). The main objects of study of this paper are the Artin groups of type An . We recall that the Artin group GAn is th...
متن کاملArithmetic of 3 and 4 Branch Point Covers
The method of choice nowadays for achieving a group G as a Galois group of a regular extension of Q(x) goes under the heading of “rigidity.” It works essentially, only, to produce Galois extensions of Q(x) ramified over 3 points. The three “rigidity” conditions (0.1) below) imply that G is generated in a very special way by two elements. Generalization of “rigidity” that considers extensions wi...
متن کاملSemi-algebraic Geometry of Braid Groups
The braid group of n-strings is the group of homotopy types of movements of n distinct points in the 2-plane R. It was introduced by E. Artin [1] in 1926 in order to study knots in R. He gave a presentation of the braid group by generators and relations, which are, nowadays, called the Artin braid relations. Since then, not only in the study of knots, the braid groups appear in several contexts...
متن کامل