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First non-zero terms for the Taylor expansion at 1 of the Conway potential function

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Abstract

The Conway potential function ∇ L (t 1,...,t l ) of an ordered oriented link L = L 1 ∪ L 2 ∪ ... ∪ L l ⊂ S 3 is considered. In general, this function is not determined by the linking numbers and the Conway potential functions of the components. However, the first two nonzero terms of the Taylor expansion at the point 1 of the function ∇ L are determined by the linking numbers only. We give the explicit formulas for these terms using summation over trees with l vertices.

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References

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia

    A. Yu. Buryak

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  1. A. Yu. Buryak
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Additional information

Original Russian Text © A.Yu. Buryak, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 1, pp. 57–59.

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Buryak, A.Y. First non-zero terms for the Taylor expansion at 1 of the Conway potential function. Moscow Univ. Math. Bull. 66, 41–43 (2011). https://doi.org/10.3103/S0027132211010086

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  • DOI: https://doi.org/10.3103/S0027132211010086

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