Twisted virtual biracks and their twisted virtual link invariants
arXiv:1105.5663
Abstract
A virtual link can be understood as a link in a trivial I-bundle over an orientable compact surface with genus. A twisted virtual link is a link in a trivial I-bundle over a not-necessarily orientable compact surface. A twisted virtual birack is an algebraic structure with axioms derived from the twisted virtual Reidemeister moves. We extend a method previously used with racks and biracks to the twisted case to define computable invariants of twisted virtual links using finite twisted virtual biracks with birack rank . As an application, we classify twist structures on the virtual Hopf link.
11 pages; Version 2 includes changes suggested by referee. To appear in Topol. Appl