Conway polynomial and Magnus expansion

Duzhin, S.

doi:10.1090/S1061-0022-2012-01207-0

Conway polynomial and Magnus expansion
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by S. V. Duzhin
Translated by: the author

St. Petersburg Math. J. 23 (2012), 541-550

DOI: https://doi.org/10.1090/S1061-0022-2012-01207-0

Published electronically: March 2, 2012

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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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