Differences of Alexander polynomials for knots caused by a single crossing change

摘要

Kondo and Sakai independently gave a characterization of Alexander polynomials for knots which are transformed into the trivial knot by a single crossing change. The first author gave a characterization of Alexander polynomials for knots which are transformed into the trefoil knot (and into the figure-eight knot) by a single crossing change. In this note, we will give a characterization of Alexander polynomials for knots which are transformed into the IO132 knot (and into the (5,2)-torus knot) by a single crossing change. Moreover, this method can be applied for knots with monic Alexander polynomials.