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

Matt Greenwood·Xiao-Song Lin
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Abstract

We prove that the knot invariant induced by a $\Bbb Z$-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 $\Bbb Z$-homology 3-sphere invariant of order 5. This result agrees with a conjecture of Rozansky based on physical predictions about the asymptotic behavior of Witten's Chern-Simons path integral.

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Matt Greenwood, Xiao-Song Lin. 1995-06-01. On Vassiliev knot invariants induced from finite type 3-manifold invariants. https://arxiv.org/abs/q-alg/9506001

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