Search results for "Braid"
showing 10 items of 44 documents
The proof of Birman’s conjecture on singular braid monoids
2003
Let B_n be the Artin braid group on n strings with standard generators sigma_1, ..., sigma_{n-1}, and let SB_n be the singular braid monoid with generators sigma_1^{+-1}, ..., sigma_{n-1}^{+-1}, tau_1, ..., tau_{n-1}. The desingularization map is the multiplicative homomorphism eta: SB_n --> Z[B_n] defined by eta(sigma_i^{+-1}) =_i^{+-1} and eta(tau_i) = sigma_i - sigma_i^{-1}, for 1 <= i <= n-1. The purpose of the present paper is to prove Birman's conjecture, namely, that the desingularization map eta is injective.
Finite Braid Groups for the SU(2) Knizhnik Zamolodchikov Equation
1995
We consider the monodromy representations of the mapping class group B 4 of the 2-sphere with 4 punctures acting in the solutions space of the zu(2) Knizhnik-Zamolodchikov equation [3] (note that the monodromy representations of the braid group have a more general geometric definition [4]).
Generalized Braid Groups and Mapping Class Gropus
1997
Given a chord system of D2, we associate a generalized braid group, a surface and a homomorphism from this braid group to the mapping class group of the surface. We disprove a conjecture stated in an article by Perron and Vannier by showing that generally this homomorphism is not injective.
Hurwitz spaces of coverings with two special fibers and monodromy group a Weyl group of typeBd
2012
f! Y; where is a degree-two coverings with n1 branch points and branch locus D and f is a degree-d coverings with n2 points of simple branching and two special points whose local monodromy is given by e and q, respectively. Furthermore the covering f has monodromy group Sd and f. D /\ D fD? where D f denotes the branch locus of f . We prove that the corresponding Hurwitz spaces are irreducible under the hypothesis n2 s r dC 1.
Metric properties of the group of area preserving diffeomorphisms
2001
Area preserving cliffeoinorpliisms of the 2-disk which are identity near the boundary form a group D2 wllich can be equipped, usin-g tlhe L2nlorm on its Lie algebra, with a right invariant metric. Witll tllis metric the diameter of D2 is infinite. In this paper we sl-iow that D2 contains quasiisometric embeddings of any finitely generated free group and any finitely generated abelian free group.
The conjugacy problem in subgroups of right-angled Artin groups
2009
We prove that the conjugacy problem in right-angled Artin groups (RAAGs), as well as in a large and natural class of subgroups of RAAGs, can be solved in linear-time. This class of subgroups contains, for instance, all graph braid groups (i.e. fundamental groups of configuration spaces of points in graphs), many hyperbolic groups, and it coincides with the class of fundamental groups of ``special cube complexes'' studied independently by Haglund and Wise.
Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
1999
It is known that a number of algebraic properties of the braid groups extend to arbitrary finite Coxeter-type Artin groups. Here we show how to extend the results to more general groups that we call Garside groups. Define a Gaussian monoid to be a finitely generated cancellative monoid where the expressions of a given element have bounded lengths, and where left and right lowest common multiples exist. A Garside monoid is a Gaussian monoid in which the left and right lowest common multiples satisfy an additional symmetry condition. A Gaussian group is the group of fractions of a Gaussian monoid, and a Garside group is the group of fractions of a Garside monoid. Braid groups and, more genera…
A note on coverings with special fibres and monodromy group $ S_{d}$
2012
We consider branched coverings of degree over with monodromy group , points of simple branching, special points and fixed branching data at the special points, where is a smooth connected complex projective curve of genus , and , are integers with . We prove that the corresponding Hurwitz spaces are irreducible if .
Braiding minimal sets of vector fields
2002
We extend a classical but fundamental theorem of knot and braid theories to describe the geometry of nonsingular minimal sets of 3-dimensional flows.
Conjugacy problem for braid groups and Garside groups
2003
We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee. This algorithm can be applied not only to braid groups, but to all Garside groups (which include finite type Artin groups and torus knot groups among others).