In this paper we explore natural connections among extraspecial 2-groups, almost-complex structures, unitary representations of the braid group and the Greenberger-Horne-Zeilinger (GHZ) states. We first present new representations of extraspecial 2-groups in terms of almost-complex structures and use them to derive new unitary braid representations as extensions of representations of the extras...

in this research, a braiding-pultrusion production line is developed by modifying a conventional textile maypole braiding machine and adding it to a pultrusion line for production of braid-pultruded (bp) composite rods. in order to evaluate the mechanical properties of bp rods and study the effect of some braiding parameters, they were produced with different braid roving linear densities and b...

In this paper we investigate certain moduli spaces (\Hurwitz spaces") of branched covers of the Riemann sphere S 2 , and representations of nite index subgroups of the spherical braid group which arise from these Hurwitz spaces. (By spherical braid group, we mean the group of braids in the 2-sphere; we will refer to the more classical group of braids in the plane as the planar braid group.) Hur...

This article surveys many standard results about the braid group, with emphasis on simplifying the usual algebraic proofs. We use van der Waerden’s trick to illuminate the Artin-Magnus proof of the classic presentation of the braid group considered as the algebraic mapping-class group of a disc with punctures. We give a simple, new proof of the σ1-trichotomy for the braid group, and, hence, rec...

Consider the unit ball, B = D × [0, 1], containing n unknotted arcs a1, a2, . . . , an such that the boundary of each ai lies in D × {0}. The Hilden (or Wicket) group is the mapping class group of B fixing the arcs a1 ∪ a2 ∪ . . . ∪ an setwise and fixing D × {1} pointwise. This group can be considered as a subgroup of the braid group. The pure Hilden group is defined to be the intersection of t...

We describe a new monoid structure for braid groups associated with finite Coxeter systems. This monoid shares with the classical positive braid monoid its crucial algebraic properties: the monoid satisfies Öre’s conditions and embeds in its group of fractions, it admits a nice normal form, it can be used to construct braid group actions on categories... It also provides a new presentation for ...

In Vassiliev theory, there is a natural monoid homo-morphism from n-strand singular braids to the group algebra of n-strand braid group. J. Birman conjectured that this monoid homomorphism is injective. We show that the monoid homomor-phism is injective on braids with up to three singularities and that Birman's conjecture is equivalent to that singular braids are dis-tinguishable by Vassiliev b...

In this paper, we construct the Lusztig symmetries for quantum Borcherds-Bozec algebra Uq(g) and its weight module M∈O, on which generators with real indices of act nilpotently. We show that these satisfy defining relations braid group, associated to Uq(g), gives a group action M.