Virtual Knot Invariants from Group Biquandles and Their Cocycles
Geometric Topology
2007-05-23 v1 Quantum Algebra
Abstract
A group-theoretical method, via Wada's representations, is presented to distinguish Kishino's virtual knot from the unknot. Biquandles are constructed for any group using Wada's braid group representations. Cocycle invariants for these biquandles are studied. These invariants are applied to show the non-existence of Alexander numberings and checkerboard colorings.
Cite
@article{arxiv.math/0703594,
title = {Virtual Knot Invariants from Group Biquandles and Their Cocycles},
author = {J. Scott Carter and Mohamed Elhamdadi and Masahico Saito and Daniel S. Silver and Susan G. Williams},
journal= {arXiv preprint arXiv:math/0703594},
year = {2007}
}
Comments
14 pages, 8 figures