Andrew Bartholomew, Roger Fenn
Published 2006-10-16Version 1
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$\times$2 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.
Comments: 21 pages, 13 figures, accepted by JKTR
Quaternion Algebras and Invariants of Virtual Knots and Links I: The Elliptic Case
On Alexander-Conway Polynomials for Virtual Knots and Links
A Functorial Map from Virtual Knots to Classical Knots and Generalisations of Parity
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