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

Greenwood, Matt; Lin, Xiao-Song

doi:10.1090/S0002-9947-99-02139-X

On Vassiliev knot invariants induced from finite type 3-manifold invariants
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by Matt Greenwood and Xiao-Song Lin PDF

Trans. Amer. Math. Soc. 351 (1999), 3659-3672 Request permission

Abstract:

We prove that the knot invariant induced by a $\mathbb {Z}$-homology 3-sphere invariant of order $\leq k$ in Ohtsuki’s sense, where $k\geq 4$, is of order $\leq k-2$. The method developed in our computation shows that there is no $\mathbb {Z}$-homology 3-sphere invariant of order 5.

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