DOI: 10.1017/s0004972726101439 ISSN: 0004-9727
EXPLICIT FORMULAE FOR THE ALEXANDER POLYNOMIAL OF PRETZEL KNOTS
YURY BELOUSOVAbstract
We provide explicit formulae for the Alexander polynomial of pretzel knots and establish several immediate corollaries, including the characterisation 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.