Representing knots by filling Dehn spheres

TL;DR

This paper demonstrates that any knot or link in a 3-manifold can be decomposed using filling Dehn spheres, providing new tools for studying branched coverings and an algorithm for computing related diagrams.

Contribution

It introduces a method to decompose knots with filling Dehn spheres and provides an algorithm to compute Johansson diagrams from branched coverings.

Findings

Any knot or link can be decomposed by a filling Dehn sphere.

An algorithm for computing Johansson diagrams from branched coverings is provided.

Implications for the study of branched coverings over knots and links.

Abstract

We prove that any knot or link in any 3-manifold can be nicely decomposed (splitted) by a filling Dehn sphere. This has interesting consequences in the study of branched coverings over knots and links. We give an algorithm for computing Johansson diagrams of filling Dehn surfaces out from coverings of 3-manifolds branched over knots or links.