Related papers: Thurston's Operations on the Braid Groups

The topological model for quantum computation is an inherently fault-tolerant model built on anyons in topological phases of matter. A key role is played by the braid group, and in this survey we focus on a selection of ways that the…

In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…

We give a method for constructing an interactive art piece which illustrates two different definitions of the braid groups, along with their faithful action on the free group. The box also demonstrates how all motions of points in the plane…

The issues involved in a determination of the baryon resonance spectrum in lattice QCD are discussed. The variational method is introduced and the need to construct a sufficient basis of interpolating operators is emphasised. The…

In this paper we study multilinear morphisms between commutative group schemes and the associated tensor constructions. We will also do some explicit calculations and give examples that show that this theory behaves in a way that one would…

The common approach to topological quantum computation is to implement quantum gates by adiabatically moving non-Abelian anyons around each other. Here we present an alternative perspective based on the possibility of realizing the exchange…

The design and implementation of large sets of spatially-extended, gauge-invariant operators for use in determining the spectrum of baryons in lattice QCD computations are described. Group-theoretical projections onto the irreducible…

We will show the raitonality of some twisted symmetric group actions.

We consider two operations on an edge of an embedded graph (or equivalently a ribbon graph): giving a half-twist to the edge and taking the partial dual with respect to the edge. These two operations give rise to an action of S_3^{|E(G)|},…

This article is about Artin's braid group and its role in knot theory. We set ourselves two goals: (i) to provide enough of the essential background so that our review would be accessible to graduate students, and (ii) to focus on those…

We study the class of groups generated by automata that act essentially freely on the boundary of a rooted tree. In the process we establish and discuss some general tools for determining if a group belongs to this class, and explore the…

Binary operations on algebras of observables are studied in the quantum as well as in the classical case. It is shown that certain natural compatibility conditions with the associative product imply the properties which usually are…

The design and implementation of large sets of spatially extended baryon operators for use in lattice simulations are described. The operators are constructed to maximize overlaps with the low-lying states of interest, while minimizing the…

We shed some light on the problem of determining the orbits of the braid group action on semiorthonormal bases of Mukai lattices as considered in \cite{GK04} and \cite{GO1}. We show that there is an algebraic (and in particular algorithmic)…

We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop like generators are found for the algebra which satisfy…

We introduce and study structured enhancement of the notion of a crossed simplicial group, which we call an operadic crossed simplicial group. We show that with each operadic crossed simplicial group one can associate a certain operad in…

A braided Frobenius algebra is a Frobenius algebra with braiding that commutes with the operations, that are related to diagrams of compact surfaces with boundary expressed as ribbon graphs. A heap is a ternary operation exemplified by a…

Topological gauge theories in four dimensions which admit surface operators provide a natural framework for realizing homological knot invariants. Every such theory leads to an action of the braid group on branes on the corresponding moduli…

We prove a 1966 conjecture of Tate concerning the Artin-Tate pairing on the Brauer group of a surface over a finite field, which is the analogue of the Cassels-Tate pairing. Tate asked if this pairing is always alternating and we find an…

This article is a survey on the braid groups, the Artin groups, and the Garside groups. It is a presentation, accessible to non-experts, of various topological and algebraic aspects of these groups. It is also a report on three points of…