English

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