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4 papers · 1 filter
Quaternionic Invariants of Virtual Knots and Links
Andrew Bartholomew, Roger Fenn
In this paper we define and give examples of a family of polynomial invariants of virtual knots and links. They arise by considering certain 22 matrices with entries in a p…
Quaternion Algebras and Invariants of Virtual Knots and Links II: The Hyperbolic Case
Steven Budden, Roger Fenn
Let be invertible, non-commuting elements of a ring . Suppose that is also invertible and that the equation called the fundamental equation is…
Weyl Algebras and Knots
Roger Fenn, Vladimir Turaev
In this paper we push forward results on the invariant -module of a virtual knot investigated by the first named author where is the algebra with two invertibl…
Virtual Knot Theory --Unsolved Problems
Roger Fenn, Louis H. Kauffman, Vassily O. Manturov
This paper is an introduction to the theory of virtual knots and links and it gives a list of unsolved problems in this subject.