Daria Aksenova, String links and lanterns

This is a talk from the conference Geometry and topology of 3-manifolds, September 17-21, 2022 We present the monoids of lanterns, where a lantern with n bands is an embedding of a framed 2- sphere with n holes into the 3-sphere. We relate these monoids to the monoids of string links, where a string link with k strands is a generalization of a braid with k strands, namely an embedding of k segments into a solid cylinder satisfying some properties. In particular, we describe an isomorphism between the monoid of lanterns with n 1 bands and the monoid of framed string links with n strands, which generalizes the well-known bijection for n=1 between knotted bands and one-strand framed string links.