Quaternionic Invariants of Virtual Knots and Links

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$\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.

21 pages, 13 figures, accepted by JKTR

Cited by in corpus (2)

• Virtual Knot Invariants from Group Biquandles and Their Cocycles
• Quaternion Algebras and Invariants of Virtual Knots and Links II: The Hyperbolic Case