A note on geometric constructions of bi-invariant orderings

Details A note on geometric constructions of bi-invariant orderings A note on geometric constructions of bi-invariant orderings

2010-05-21

arxiv.org/abs/1005.3870v2

Topology and its Applications,158 (2011) 690-696

Mathematics

Geometric Topology

10 pages, no figures; add more explanations for the relationship to the classical construction

Scientific paper

10.1016/j.topol.2011.01.015

We construct bi-invariant total orderings of residually torsion-free nilpotent groups by using Chen's iterated integrals. This construction can be seen as a generalization of the Magnus ordering of the free groups, and equivalent to the classical construction which uses an iteration of central extensions. Our geometric construction provides a connection between bi-orderings and the rational homotopy theory.

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