Invariants of knot diagrams and relations among Reidemeister moves
By Olof-Petter OEstlund. 2000
51 citations recorded by the source corpus.
In this paper a classification of Reidemeister moves, which is the most refined, is introduced. In particular, this classification distinguishes some Ω3-moves that only differ in how the three strands that are involved in the move are ordered on the knot. To transform knot diagrams of isotopic knots into each other one must in general use Ω3-moves of at least two different classes. To show this, knot diagram invariants that jump only under Ω3-moves are introduced. Knot diagrams of isotopic knots can be connected by a sequence of Reidemeister moves of only six, out of the total of 24, classes. This result can be applied in knot theory to simplify proofs of invariance of diagrammatical knot invariants. In particular, a criterion for a function on Gauss diagrams to define a knot invariant is presented.
Subfields: Artificial Intelligence, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7aecf1cd852ab66c83e09eeabb57f6977102d5c9
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Quantum Topology (2009, background): “The number of Ω3 moves used by Östlund [5] is also two, but his classification of Ω3 moves works only for knots and is nonlocal (depending on the cyclic order of the fragments along the knot).”