Integral positive (negative) quandle cocycle invariants are trivial for knots

Zhiyun Cheng, Hongzhu Gao

In this note we prove that for any finite quandle $X$ and any 2-cocycle $ϕ\in Z^2_{Q\pm}(X; \mathds{Z})$, the cocycle invariant ${\Phi }_{\varphi }^{\pm }(K)$ is trivial for all knots $K$.