Conway polynomial and Magnus expansion

Details Conway polynomial and Magnus expansion Conway polynomial and Magnus expansion

2010-01-14

arxiv.org/abs/1001.2500v2

Mathematics

Geometric Topology

12 pages, several figures. Typos and inaccuracies corrected, bibliography updated, an acknowledgement added

Scientific paper

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. We describe explicitly the resulting mapping from horizontal chord diagrams on 3 strands to univariate polynomials and evaluate it on the Drinfeld associator obtaining, conjecturally, a beautiful generating function whose coefficients are integer combinations of multiple zeta values.

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