This article is cited in 3 papers

A formula for the generalized Sato–Levine invariant

P. M. Akhmet'ev^a, I. Maleshich^b, D. Repovš<sup>c

a</sup> Steklov Mathematical Institute, Russian Academy of Sciences
^b Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation
^c University of Ljubljana

Abstract: Let $W$ be the generalized Sato–Levine invariant, that is, the unique Vassiliev invariant of order 3 for two-component links that is equal to zero on double torus links of type $(1,k)$. It is proved that
$$ W=\beta-\frac{k^3-k}6\,, $$
where $\beta$ is the invariant of order 3 proposed by Viro and Polyak in the form of representations of Gauss diagrams and $k$ is the linking number.

UDC: 515.1

MSC: 57M27, 57M25

Received: 03.06.1999 and 23.05.2000

DOI: 10.4213/sm533

 English version: Sbornik: Mathematics, 2001, 192:1, 1–10

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