Unknotting surface links which are coverings of a trivial torus knot

TL;DR

This paper investigates the unknotting numbers of surface links in 4-space that are represented as branched coverings over a standard torus, providing specific cases where these numbers are determined.

Contribution

It introduces the concept of torus-covering links and determines unknotting numbers for certain cases, advancing understanding of surface link complexity.

Findings

Unknotting numbers are determined for specific torus-covering links.

The paper establishes methods to analyze unknotting numbers in this context.

Abstract

We consider surface links in the 4-space which are presented by the form of simple branched coverings over the standard torus, which we call torus-covering links. In this paper, we study unknotting numbers of torus-covering links. In some cases, we can determine the unknotting numbers.