Finite type invariant

Summary

A finite type invariant, or Vassiliev invariant, is a knot invariant whose extension to knots with double points vanishes once there are enough double points. They behave like polynomials on the space of knots, with the number of double points playing the role of the degree. Many classical invariants, such as the coefficients of the Conway polynomial and of the suitably expanded Jones polynomial, are of finite type. The Kontsevich integral is universal among rational finite type invariants.