Distinguishing mutant pretzel knots in concordance

Abstract

We prove that many pretzel knots of the form $P(2n,m,-2n\pm 1,-m)$ are not topologically slice, even though their positive mutants $P(2n,-2n\pm 1,m,-m)$ are ribbon. We use the sliceness obstruction of Kirk and Livingston related to the twisted Alexander polynomials associated to prime power cyclic covers of knots.

arXiv comment20 pages, 2 very large matrices