On some ternary operations in knot theory

Maciej Niebrzydowski. "On some ternary operations in knot theory." Fundamenta Mathematicae 225.0 (2014): 259-276. <http://eudml.org/doc/283252>.

@article{MaciejNiebrzydowski2014,
abstract = {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.},
author = {Maciej Niebrzydowski},
journal = {Fundamenta Mathematicae},
keywords = {ternary operation; core group; knot group; bol loop; Moufang loop; extra loop; Latin cube},
language = {eng},
number = {0},
pages = {259-276},
title = {On some ternary operations in knot theory},
url = {http://eudml.org/doc/283252},
volume = {225},
year = {2014},
}

TY - JOUR
AU - Maciej Niebrzydowski
TI - On some ternary operations in knot theory
JO - Fundamenta Mathematicae
PY - 2014
VL - 225
IS - 0
SP - 259
EP - 276
AB - 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.
LA - eng
KW - ternary operation; core group; knot group; bol loop; Moufang loop; extra loop; Latin cube
UR - http://eudml.org/doc/283252
ER -