Tangle Surgeries Which Preserve Jones-Type Polynomials

Abstract

Using an argument from statistical mechanics, V. Jones has given a new method for constructing pairs of links with identical skein polynomials. We give a more general construction and use it to provide a simple proof of a theorem of Traczyk's involving rotors of links. Several examples are given of pairs of knots with coincident skein polynomials and small crossing number.