Virtual and welded periods of classical knots

TL;DR

The paper proves that all virtual or welded symmetries of classical knots are actually classical symmetries, implying only finitely many such symmetries exist for any classical knot.

Contribution

It demonstrates that virtual and welded periods of classical knots are realizable as classical periods, establishing a connection between virtual/welded and classical symmetries.

Findings

Any virtual or welded period of a classical knot can be realized as a classical period.

Classical knots have only finitely many virtual or welded periods.

Virtual and welded symmetries do not introduce new types of symmetries beyond classical ones.

Abstract

We show that any virtual or welded period of a classical knot $K$ can be realized as a classical period. A direct consequence is that a classical knot admits only finitely many virtual or welded periods.