Knot theory, Jones polynomial and quantum computing

Knot theory emerged in the nineteenth century for needs of physics and chemistry as these needs were understood those days. After that the interest of physicists and chemists was lost for about a century. Nowadays knot theory has made a comeback. Knot, theory and other areas of topology are no more considered as abstract areas of classical mathematics remote from anything of practical interest. They have made deep impact on quantum field theory, quantum computation and complexity of computation.