Clasper Presentations of Habegger-Lin’s Action on String Links Habegger and Lin gave a classification of the link-homotopy classes of links as the link-homotopy classes of string links modulo the actions of conjugations and partial conjugations for string links. In this paper, we calculate the actions of the partial conjugations and the conjugations explicitly for 4- and 5-component string links which gave classifications (presentations) of the link-homotopy classes of 4- and 5-component links. As an application, we can run Habegger and Lin’s algorithm which determines whether given two links are link-homotopic or not for 4- and 5-component links.

"Clasper Presentations of Habegger-Lin’s Action on String Links" by Yuka Kotorii and Atsuhiko Mizusawa. #ExperimentalMath #LinkHomotopy #MathSky