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

1995/06/01 by Greenwood, Matt, Lin, Xiao-Song
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.q-alg/9506001

Abstract

We prove that the knot invariant induced by a \Bbb Z-homology 3-sphere invariant of order ≤ k in Ohtsuki's sense, where k≥ 4, is of order ≤ 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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