EXPLICIT FORMULAE FOR THE ALEXANDER POLYNOMIAL OF PRETZEL KNOTS

Bulletin of the Australian Mathematical Society 2026 Open access

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Authors: Y. Belousov
DOI: 10.1017/s0004972726101439
Cited by: 0
References: 11

Abstract

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.

Fields of Study & Subjects

Mathematics and Applications Advanced Mathematical Theories and Applications Advanced Combinatorial Mathematics

Publication details

Journal / source
Bulletin of the Australian Mathematical Society
Publisher
Cambridge University Press (CUP)
Pages
1–11
Publication date
24 June 2026
Language
EN