English

Quaternionic Invariants of Virtual Knots and Links

Geometric Topology 2007-05-23 v1 Rings and Algebras

Abstract

In this paper we define and give examples of a family of polynomial invariants of virtual knots and links. They arise by considering certain 2×\times2 matrices with entries in a possibly non-commutative ring, for example the quaternions. These polynomials are sufficiently powerful to distinguish the Kishino knot from any classical knot, including the unknot.

Keywords

Cite

@article{arxiv.math/0610484,
  title  = {Quaternionic Invariants of Virtual Knots and Links},
  author = {Andrew Bartholomew and Roger Fenn},
  journal= {arXiv preprint arXiv:math/0610484},
  year   = {2007}
}

Comments

21 pages, 13 figures, accepted by JKTR

R2 v1 2026-07-22T17:44:21.281Z