Commensurability classes containing three knot complements

TL;DR

This paper presents an infinite family of hyperbolic knot complements, each sharing a commensurability class with exactly three knot complements, highlighting a new phenomenon in the classification of knot complements.

Contribution

It introduces the first known infinite family of hyperbolic knot complements with exactly three in their commensurability classes, expanding understanding of knot complement classifications.

Findings

Identifies an infinite family of hyperbolic knot complements with three in their class

Demonstrates the existence of such classes beyond previously known examples

Provides new insights into the structure of commensurability classes in knot theory

Abstract

This paper exhibits an infinite family of hyperbolic knot complements that have three knot complements in their respective commensurability classes.