paper

Explicit Formulas for the Alexander Polynomial of Pretzel Knots

arXiv:2502.10370 · doi:10.1017/S0004972726101439

Abstract

We provide explicit formulas for the Alexander polynomial of pretzel knots and establish several immediate corollaries, including the characterization of pretzel knots with a trivial Alexander polynomial. As an application, we construct a new family of knots that are topologically slice but not smoothly slice.

9 pages, 3 figures; v4: revised exposition, added an appendix