Journal of the Mathematical Society of Japan

A functor-valued extension of knot quandles

Tetsuya ITO

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For an oriented knot $K$, we construct a functor from the category of pointed quandles to the category of quandles in three different ways. This functor-valued invariant of a knot is an extension of the knot quandle. We also extend the quandle cocycle invariants of knots by using these quandle-valued invariants, and study their properties.

Article information

J. Math. Soc. Japan, Volume 64, Number 4 (2012), 1147-1168.

First available in Project Euclid: 29 October 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds

quandle knot quandle homology cocycle invariant quandle invariant functor


ITO, Tetsuya. A functor-valued extension of knot quandles. J. Math. Soc. Japan 64 (2012), no. 4, 1147--1168. doi:10.2969/jmsj/06441147.

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