The n-th braid group consist of all different ways n strings can be braided. The generators are all the over-crossings and under-crossings of neighbouring strings. They can be also imagined as world lines of n particles in 2 dimensions which changes its order.

Examples

The generators σ_i^+ 1 and σ_i^− 1:

Image:braid.jpg And the transformation like: Image:knot.jpg is not a braid.

Applications

The braid group plays key-role in the topological computing.

Category:Mathematical Structure Category:Models of Quantum Computation