A generalization of the Sato-Levine invariant
by
Jože Malešič
Institute of Maths, Physics and Astronomy, University of Ljubljana, Slovenia

An invariant \beta for two-component links is constructed by means of Viro-Polyak representations of Gauss diagrams. Its order equals to 3 in the sense of Vassiliev theory. The invariant \beta changes its value following a certain rule when the Matveev (= generalized 3rd type Reidemeister) move is applied. That rule implies the following facts:

1. For links with the linking number equal to 0 the invariant \beta coincides with the Sato-Levine invariant.
2. For doubled knots the Akhmetiev formula
   

   \beta = 2vk

   takes place where k denotes the linking number and v is the unique Vassiliev invariant of order 2 having the value 1 on the trefoil knot.

Date received: June 28, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadc-14.