DISTINGUISHING MUTANTS BY KNOT POLYNOMIALS

We consider the problem of distinguishing mutant knots using invariant s of their satellites. We show, by explicit calculation, that the Homf ly polynomial of the 3-parallel (and hence the related quantum invaria nts) will distinguish some mutant pairs. Having established a conditio n on the colouring module which forces a quantum invariant to agree on mutants, we explain several features of the difference between the Ho mfly polynomials of satellites constructed from mutants using more gen eral patterns. We illustrate this by our calculations; from these we i solate some simple quantum invariants, and a framed Vassiliev invarian t of type 11, which distinguish certain mutants, including the Conway and Kinoshita-Teresaka pair.