Infinitely many prime knots with the same Alexander invariants

TL;DR

This paper demonstrates the existence of infinitely many prime knots sharing the same Alexander invariants, using elementary methods based on a specific subclass of pretzel knots with three tassels.

Contribution

It introduces new infinite families of prime knots with identical Alexander invariants, constructed through elementary techniques involving pretzel knots.

Findings

Existence of infinitely many prime knots with identical Alexander invariants.

Construction of these knots using elementary methods and pretzel knots.

Each family contains infinitely many distinct knots.

Abstract

We revisit the issue of the existence of infinitely many distinct prime knots with the same Alexander invariant. We present infinitely many distinct families, each family made up of infinitely many distinct knots. Within each family, the Alexander invariant is the same. Unlike other examples in the literature, ours are elementary and based on a sub-collection of pretzel knots with three tassels.