We explore the relation between topological and quantum mechanical entanglement. We first emphasize on the similarities and differences between these two concepts. Then we show that a proper context for making such a connection is via the braid group operators. We then provide some specific examples and calculate the entangling power of braid group operators. Although our results shows some pat...

Braided Thompson’s groups are finitely presented groups introduced by Brin and Dehornoy which contain the ordinary braid groups Bn, the finitary braid group B∞ and Thompson’s group F as subgroups. We describe some of the metric properties of braided Thompson’s groups and give upper and lower bounds for word length in terms of the number of strands and the number of crossings in the diagrams use...

Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants ([10]), stable on deformations. From this factorization, one can compute the fundamental group of the complement of the branch curve, either in C or in CP. In this articl...

The path integral approach to representing braid group is generalized for particles with spin. Introducing the notion of charged winding number in the super-plane, we represent the braid group generators as homotopically constrained Feynman kernels. In this framework, super Knizhnik-Zamolodchikov operators appear naturally in the Hamiltonian, suggesting the possibility of spinning nonabelian an...

The braid group with its conjugacy problem is one of the recent hot issues in cryptography. At CT-RSA 2001, Anshel, Anshel, Fisher, and Goldfeld proposed a commutator key agreement protocol (KAP) based on the braid groups and their colored Burau representation. Its security is based on the multiple simultaneous conjugacy problem (MSCP) plus a newly adopted key extractor. This article shows how ...

An overview of the braid group techniques in the theory of algebraic surfaces from Zariski to the latest results is presented. An outline of the Van Kampen algorithm for computing fundamental groups of complements of curves and the modification of Moishezon-Teicher regarding branch curves of generic projections are given. The paper also contains a description of a quotient of the braid group, n...