Twisted virtual biracks and their twisted virtual link invariants
Geometric Topology
2012-12-03 v2 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1105.5663,
title = {Twisted virtual biracks and their twisted virtual link invariants},
author = {Jessica Ceniceros and Sam Nelson},
journal= {arXiv preprint arXiv:1105.5663},
year = {2012}
}
Comments
11 pages; Version 2 includes changes suggested by referee. To appear in Topol. Appl