On some ternary operations in knot theory

• Autorzy: Maciej Niebrzydowski
• Języki publikacji: EN

Abstrakty

EN

We introduce a way to color the regions of a classical knot diagram using ternary operations, so that the number of colorings is a knot invariant. By choosing appropriate substitutions in the algebras that we assign to diagrams, we obtain the relations from the knot group, and from the core group. Using the ternary operator approach, we generalize the Dehn presentation of the knot group to extra loops, and a similar presentation for the core group to the variety of Moufang loops.

Kategorie tematyczne

• 57M27: Invariants of knots and 3-manifolds
• 08A62: Finitary algebras
• 08C05: Categories of algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 225
• Numer: 1
• Strony: 259-276

Daty

wydano

2014

Twórcy

autor

Maciej Niebrzydowski

• Department of Mathematics, University of Louisiana at Lafayette, 217 Maxim D. Doucet Hall, 1403 Johnston Street, Lafayette, LA 70504-1010, U.S.A.

Identyfikatory

DOI

10.4064/fm225-1-12