# Relationship between quandle shadow cocycle invariants and Vassiliev invariants

## TL;DR

This paper establishes a connection between quandle shadow cocycle invariants and Vassiliev invariants, showing that the coefficients of certain quandle invariants are Vassiliev invariants for braids.

## Contribution

It proves that the coefficients of the finite perturbative expansion of specific quandle shadow cocycle invariants are Vassiliev invariants, answering a question posed by T. Ohtsuki.

## Key findings

- Coefficients of quandle shadow cocycle invariants are Vassiliev invariants.
- The result applies to invariants defined by $( ext{Z}/p ext{Z})$-Laurent polynomial quandles.
- Establishes a link between quantum invariants and finite-type invariants.

## Abstract

As one of the problems in his list [20], T. Ohtsuki proposed to study relations between quandle cocycle invariants and quantum invariants. The aim of this paper is to answer one of those questions. We prove that the coefficient of the finite perturbative expansion of the quandle shadow cocycle invariant defined by $(\Z /p\Z)$-Laurent polynomial quandle is Vassiliev invariant for any braids.