On the group of ring motions of an H-trivial link

TL;DR

This paper computes a presentation for the group of ring motions of a specific H-trivial link configuration, advancing understanding of link motion groups in 3D space.

Contribution

It provides the first explicit presentation for the ring motion group of a split union involving a Hopf link and a Euclidean circle, extending previous work on simpler cases.

Findings

Derived a presentation for the ring motion group of the specified link

Analyzed a short exact sequence of ring motion groups in $ ext{R}^3$

Established a foundation for future computations of H-trivial link motion groups

Abstract

In this paper we compute a presentation for the group of ring motions of the split union of a Hopf link with Euclidean components and a Euclidean circle. A key part of this work is the study of a short exact sequence of groups of ring motions of general ring links in $\mathbb{R}^3$. This sequence allowed us to build the main result from the previously known case of the ring group with one component, which a particular case of the ring groups studied by Brendle and Hatcher. This work is a first step towards the computation of a presentation for groups of motions of H-trivial links with an arbitrary number of components.