Implementation of the Habegger–Lin decision algorithm

Abstract

Habegger and Lin gave a classification of link-homotopy classes of links in terms of link-homotopy classes of string links modulo certain group actions. As an application, they constructed an algorithm for determining whether two given links are link-homotopic. In [8], we explicitly computed these group actions in the 4- and 5-component cases. Consequently, the Habegger–Lin algorithm can be effectively applied in these cases. In this paper, we present an implementation of this algorithm, available at [12], and exhibit new pairs of links that are not link-homotopic yet cannot be distinguished by Milnor’s link-homotopy invariants, called μ̄-invariants.