Scissor equivalence for torus links

TL;DR

This paper introduces a new way to measure the distance between torus links using smooth cobordisms, showing that this distance is essentially determined by their signature functions.

Contribution

It establishes that the cobordism distance for torus links can be characterized by their signature function profiles, up to a constant factor.

Findings

Cobordism distance of torus links is determined by signature functions.

Signature profiles effectively measure link differences.

Provides a new perspective on link equivalence and classification.

Abstract

This article is about a natural distance function induced by smooth cobordisms between links. We show that the cobordism distance of torus links is determined by the profiles of their signature functions, up to a constant factor.