Concordance group of virtual knots

TL;DR

This paper investigates the concordance properties of virtual knots, establishing that classical knots are virtually slice if and only if they are classically slice, and showing the embedding of classical knot concordance into virtual knot concordance.

Contribution

It proves the equivalence of classical and virtual sliceness for knots and demonstrates the embedding of classical knot concordance into virtual knot concordance group.

Findings

Classical knots are virtually slice iff they are classically slice.

The concordance group of classical knots embeds into that of long virtual knots.

Provides a link between classical and virtual knot concordance theories.

Abstract

We study concordance of virtual knots. Our main result is that a classical knot K is virtually slice if and only if it is classically slice. From this we deduce that the concordance group of classical knots embeds into the concordance group of long virtual knots.