Quaternionic Invariants of Virtual Knots and Links

Details Quaternionic Invariants of Virtual Knots and Links Quaternionic Invariants of Virtual Knots and Links

2006-10-16

arxiv.org/abs/math/0610484v1

Mathematics

Geometric Topology

21 pages, 13 figures, accepted by JKTR

Scientific paper

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.

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