On Milnor moves and Alexander polynomials of knots (Q1423467)

The authors define a local move on a knot diagram called a Milnor move of order \(n\), or \(M_n\)-move. \(M_n\)-equivalence is the equivalence relation on knots which is generated by such moves. They prove a relationship between the Alexander polynomials of \(M_n\)-equivalent knots (\(n\geq2\)). In fact, they distinguish two types of \(M_n\)-moves, which they call \(M_n^+\)- and \(M_n^-\)-moves, and they show that two knots which are \(M_n\)-equivalent are cobordant and that a knot which is \(M_n^+\)-equivalent to the trivial knot is ribbon (in both cases with \(n\geq2\)).