A note on geometric constructions of bi-invariant orderings
Geometric Topology
2011-02-07 v2 Group Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1005.3870,
title = {A note on geometric constructions of bi-invariant orderings},
author = {Tetsuya Ito},
journal= {arXiv preprint arXiv:1005.3870},
year = {2011}
}
Comments
10 pages, no figures; add more explanations for the relationship to the classical construction