QUATERNIONIC INVARIANTS OF VIRTUAL KNOTS AND LINKS

By A. Bartholomew, R. Fenn. 2006

59 citations recorded by the source corpus.

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 x 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

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8f23bd55d31a03b24cc3156d1815cd8852d54616

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In Discrete Mathematics and Combinatorics

1. Louis H. Kauffman
2. H. Dye
3. Zhiyun Cheng
4. Hongzhu Gao
5. V. Manturov

In Geometry and Topology

1. Louis H. Kauffman
2. H. Dye
3. Zhiyun Cheng
4. Hongzhu Gao
5. V. Manturov
6. Cody Armond
7. Jacob Rasmussen
8. Shelly L. Harvey

In Mathematical Physics

1. Louis H. Kauffman
2. H. Dye
3. Zhiyun Cheng
4. Hongzhu Gao
5. V. Manturov
6. Cody Armond
7. Jacob Rasmussen
8. Shelly L. Harvey

Citations in the corpus

• Minimal surface representations of virtual knots and links (2004, methodology): “Kishino’s knot is also detected by the quaternionic biquandle [ 2 ], [11].”