Artin braid group

Consider n strings, each oriented vertically from a lower to an upper "bar." If this is the least number of strings needed to make a closed braid representation of a link, n is called the braid index. A general n-braid is constructed by iteratively applying the σ_i (i = 1, ..., n - 1) operator, which switches the lower endpoints of the ith and (i + 1)th strings--keeping the upper endpoints fixed--with the ith string brought above the (i + 1)th string. If the ith string passes below the (i + 1)th string, it is denoted σ_i^(-1). The operations σ_i and σ_i^(-1) on n strings define a group known as the braid group or Artin braid group, denoted B_n.

braid | braid index | braid word | knot | link