A functor-valued extension of knot quandles

Abstract

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

17 pages, 7 figures, typos and inconsintent notations are corrected

Cited by in corpus (2)

• The classification of Wada-type representations of braid groups
• Actions of the n-strand braid groups on the free group of rank n which are similar to the Artin representation