Uniqueness of free 2-periodicities of links

TL;DR

This paper proves that two links in real projective 3-space are isotopic if their preimages in the 3-sphere are isotopic, establishing a link between link isotopy in these spaces.

Contribution

It demonstrates a correspondence between isotopic links in $ ext{RP}^3$ and their preimages in $S^3$, revealing a new property of link periodicities.

Findings

Preimages of isotopic links in $S^3$ imply isotopy in $ ext{RP}^3$

The result applies to free 2-periodic links in $ ext{RP}^3$

Establishes a criterion for link isotopy based on double coverings

Abstract

We show that if two links in the real projective 3-space $\mathbb{RP}^{3}$ have isotopic preimages in the 3-sphere $S^{3}$ by the double covering map, then they are themselves isotopic in $\mathbb{RP}^{3}$.