QUANDLE HOMOMORPHISMS OF KNOT QUANDLES TO ALEXANDER QUANDLES-Reference-Cited by-同舟云学术

QUANDLE HOMOMORPHISMS OF KNOT QUANDLES TO ALEXANDER QUANDLES

Published:2001-09 Issue:06 Volume:10 Page:813-821
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

INOUE AYUMU¹

Affiliation:

1. Department of Mathematics, Tokyo Institute of Technology, Oh–okayama, Meguro–ku, Tokyo, 152–8551, Japan

Abstract

A quandle is a set with a binary operation satisfying some properties. A quandle homomorphism is a map between quandles preserving the structure of their binary operations. A knot determines a quandle called a knot quandle. We show that the number of all quandle homomorphisms of a knot quandle of a knot to an Alexander quandle is completely determined by Alexander polynomials of the knot. Further we show that the set of all quandle homomorphisms of a knot quandle to an Alexander quandle has a module structure.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216501001177

Reference3 articles.

1. RACKS AND LINKS IN CODIMENSION TWO

2. Free Differential Calculus. II: The Isomorphism Problem of Groups

3. A classifying invariant of knots, the knot quandle

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