ON BRAIDS AND LINKS UP TO LINK-HOMOTOPY

Emmanuel Graff (1)

1 UNICAEN - Université de Caen Normandie

This paper deals with links and braids up to link-homotopy, studied from the viewpoint of Habiro's clasper calculus. More precisely, we use clasper homotopy calculus in two main directions. First, we define and compute a faithful linear representation of the homotopy braid group, by using claspers as geometric commutators. Second, we give a geometric proof of Levine's classification of 4-component links up to link-homotopy, and go further with the classification of 5-component links in the algebraically split case.

Mots clés: Links; Braid groups; Link-homotopy; Claspers

Domaines: Topologie géométrique [math.GT]; Théorie des groupes [math.GR]

Emmanuel Graff. ON BRAIDS AND LINKS UP TO LINK-HOMOTOPY. 2022. ⟨hal-03792805⟩