|
Organizers |
H-valued Knotoid Invariants
by
Alexander Borland
The Ohio State University
Coauthors: Thomas Kerler (The Ohio State University)
In 2011, Turaev introduced the monoid of Knotoids K. Given a ribbon Hopf algebra H together with a ribbon automorphism on H, we construct a morphism of monoids from K to H. In the case of a trivial automorphism, the construction specializes to known knot invariants that associate to a knot an element in the center of H. Moreover, when specialized to the fundamental representation of quantum sl2 our invariant reproduces Turaev's knotoid bracket polynomial with an additional parameter. The method readily implies colored versions of Tuarev's invariant as well as multi-parameter generalizations to higher rank quantum groups.
Date received: December 8, 2014
Copyright © 2014 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbjz-45.