TY - JOUR

T1 - Uncolorable Brunnian Links are Linked

AU - Kauffman, Louis H.

AU - Prasad, Devika

AU - Zhu, Claudia J.

N1 - Funding Information: Louis H. Kauffman is supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (contract no. 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation). Publisher Copyright: © 2022, Mathematical Association of America.

PY - 2022

Y1 - 2022

N2 - Summary: The topology of knots and links can be studied by examining colorings of their diagrams. We explain how to detect knots and links using the method of Fox tricoloring, and we give a new and elementary proof that an infinite family of Brunnian links are each linked. Our proof is based on the remarkable fact (which we prove) that if a link diagram cannot be tricolored then it must be linked. Our paper introduces readers to the Fox coloring generalization of tricoloring and the further algebraic generalization, called a quandle by David Joyce.

AB - Summary: The topology of knots and links can be studied by examining colorings of their diagrams. We explain how to detect knots and links using the method of Fox tricoloring, and we give a new and elementary proof that an infinite family of Brunnian links are each linked. Our proof is based on the remarkable fact (which we prove) that if a link diagram cannot be tricolored then it must be linked. Our paper introduces readers to the Fox coloring generalization of tricoloring and the further algebraic generalization, called a quandle by David Joyce.

KW - 57M25

UR - http://www.scopus.com/inward/record.url?scp=85142868696&partnerID=8YFLogxK

U2 - 10.1080/0025570X.2022.2136462

DO - 10.1080/0025570X.2022.2136462

M3 - Article

AN - SCOPUS:85142868696

VL - 95

SP - 437

EP - 451

JO - Mathematics Magazine

JF - Mathematics Magazine

SN - 0025-570X

IS - 5

ER -