A group-valued invariant of knots in the full torus

TL;DR

This paper introduces a simple, combinatorial group-theoretic method to construct sliceness obstructions for knots in the full torus, advancing tools in knot concordance studies.

Contribution

It presents a new elementary and combinatorial approach using easy-to-handle groups to produce sliceness obstructions for knots in the full torus.

Findings

Provides a new group-theoretic technique for knot sliceness obstructions.

Simplifies the process with elementary combinatorial methods.

Enhances understanding of knot concordance in the full torus.

Abstract

Knot concordance plays a crucial role in the low dimensional topology. We propose a very elementary techniques which allows one to construct a lot of sliceness obstructions for knots in the full torus. Our approach deals with group theoretical techniques; it is completely combinatorial, and the groups are very easy to deal with.