A note on geometric constructions of bi-invariant orderings

作者：Ito Tetsuya^*

来源：Topology and Its Applications, 2011, 158(5): 690-696.

DOI：10.1016/j.topol.2011.01.015

• Bi-invariant ordering
• Iterated integral
• Holonomy representation
• Rational homotopy

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.

• 出版日期2011-3-15