Author: Steffen Kionke

Topological complexity

Rummaging in the arXiv I ran across this article and the notion of topological complexity which is really appealing. The idea of topological complexity isn’t quite new, it was developed by M. Farber in a short article published in 2003 in Discrete & Computational Geometry. The article doesn’t even have a proper review on MathSciNet, … Continue reading "Topological complexity"

The group of germs at infinity of line homeomorphisms

Recently, I learned that the group G∞ of germs at +∞ of orientation preserving homeomorphisms of the real line has two remarkable properites: it is simple and left-orderable. I thought it is maybe worth to share some background on left-orderability (and why this might be interesting). Let’s start with a definition: A group G is … Continue reading "The group of germs at infinity of line homeomorphisms"