Braid group

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 $\backslash sigma\_i^\{+1\}$ and $\backslash sigma\_i^\{-1\}$: [[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. {{stub}} [[Category:Mathematical Structure]] [[Category:Models of Quantum Computation]]