Relationship between quandle shadow cocycle invariants and Vassiliev invariants of links

Sukuse Abe

Published 2018-12-30Version 1

In this study, we deduce Vassiliev invariants from quandle shadow cocycle invariants using the Alexander quandle of links. First, we relate the quandle (shadow) cocycle invariants and Vassiliev invariants of links. Second, we obtain the relation between quandle cocycle invariants and Vassiliev invariants.Third, we describe an example of $(2,n)$-torus links.Finally, we present a problem for application to surface $2$-knots. Generally, it is difficult for us to obtain Vassiliev invariants from Quandle (shadow) cocycle invariants by using Main Theorem. However, it can be obtained as shown by Example.