The monoid of singular braids
by
Joan S. Birman
Columbia University

The discovery of Vassiliev invariants of knots and links suggested a natural object to investigate: the monoid of singular braids. One obtains this monoid by adding n-1 elementary singular braids to the n-string braid group. Motivated by the mathematics of Vassiliev invariants, we tried one day to "resolve singularities" in this monoid, much as Vassiliev resolved singularities in singular knots. This presented us with a strange map from the monoid of singlar braids to the integral group ring of the braid group, and to our surprise this map turned out to be a homomorphism! In fact, more is true: it's an isomorphism onto its image. The proof of this assertion is joint work with Antal Jarai, and it will be the subject of my talk.

Date received: January 31, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaa-53.