Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Braids and homotopy groups

In this talk, we give some relations of the homotopy groups of the sphere with braids and configurations. A Brunnian braid over a manifold means a braid which becomes trivial after removing any one of its strings. One of our main results states that the higher homotopy groups of the sphere are isomorphic to the quotient of the Brunnian braids over the sphere by the Brunnian braids over the disk. Our other results state that the homotopy groups of the sphere occur as certain canonical sub-quotients of Artin braid groups.