Cosmetic banding on knots and links

TL;DR

This paper explores cosmetic bandings on knots and links, providing examples that do not change their types, and presents a hyperbolic knot with exotic surgeries that challenge existing conjectures.

Contribution

It introduces new examples of cosmetic bandings and a hyperbolic knot with exotic surgeries, countering previous conjectures in the field.

Findings

Examples of cosmetic bandings that preserve knot/link types

A hyperbolic knot with exotic chirally cosmetic surgeries

Counterexample to Bleiler-Hodgson-Weeks conjecture

Abstract

We present various examples of cosmetic bandings on knots and links, that is, bandings on knots and links leaving their types unchanged. As a byproduct, we give a hyperbolic knot which admits exotic chirally cosmetic surgeries yielding hyperbolic manifolds. This gives a counterexample to a conjecture raised by Bleiler, Hodgson and Weeks.