EXPLICIT FORMULAE FOR THE ALEXANDER POLYNOMIAL OF PRETZEL KNOTS
Abstract 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.
Authors
- Yury Belousov (ORCID: https://orcid.org/0000-0003-3999-8843)
Institutions
- International Management Institute Saint Petersburg (RU)
Publication Details
- Journal
- Bulletin of the Australian Mathematical Society
- Published
- 2026-06-24
- DOI
- https://doi.org/10.1017/s0004972726101439
- Primary Topic
- Geometric and Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Ministry of Science and Higher Education of the Russian Federation