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: And the transformation like: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