On Vassiliev knot invariants induced from finite type 3-manifold invariants

Matt Greenwood, Xiao-Song Lin

We prove that the knot invariant induced by a $\mathbb{Z}$-homology 3-sphere invariant of order $\le k$ in Ohtsuki's sense, where $k\ge 4$, is of order $\le k-2$. The method develop…