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Conway polynomial and Magnus expansion


Author: S. V. Duzhin
Translated by: the author
Original publication: Algebra i Analiz, tom 23 (2011), nomer 3.
Journal: St. Petersburg Math. J. 23 (2012), 541-550
MSC (2010): Primary 20F36
DOI: https://doi.org/10.1090/S1061-0022-2012-01207-0
Published electronically: March 2, 2012
MathSciNet review: 2896167
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Abstract: The Magnus expansion is a universal finite type invariant of pure braids with values in the space of horizontal chord diagrams. The Conway polynomial composed with the short-circuit map from braids to knots gives rise to a series of finite type invariants of pure braids and thus factors through the Magnus map. In the paper, the resulting mapping from horizontal chord diagrams on 3 strands to univariate polynomials is described explicitly and evaluated on the Drinfeld associator, which leads to a beautiful generating function whose coefficients are, conjecturally, alternating sums of multiple zeta values.


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Additional Information

S. V. Duzhin
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: duzhin@pdmi.ras.ru

DOI: https://doi.org/10.1090/S1061-0022-2012-01207-0
Keywords: Conway polynomial, Magnus expansion, Vassiliev invariants
Received by editor(s): October 3, 2010
Published electronically: March 2, 2012
Additional Notes: Supported by grants RFBR 08-01-00379-a, NSh 709.2008.1, and JSPS S-09018.
Article copyright: © Copyright 2012 American Mathematical Society