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

## Last modified:

Monday, October 26, 2015 - 17:37