Twisting Some Classes of Links

TL;DR

This paper demonstrates that by applying the twisting technique to certain classes of links, one can generate infinitely many new links within those classes, expanding the understanding of their structure.

Contribution

The paper introduces a method to produce infinite families of adequate, homogeneous, or alternative links from a single such link using the twisting technique.

Findings

Infinite families of adequate, homogeneous, and alternative links are constructed.

The classes of adequate, homogeneous, and alternative links are proven to be infinite.

The twisting technique is effective for generating new links within these classes.

Abstract

We apply the twisting technique that was first introduced in \cite{CK} and later generalized in \cite{QCQ} to obtain an infinite family of adequate, homogeneous or alternative links from a given adequate, homogeneous or alternative link, respectively. Thus we conclude that these three classes of links are infinite.