The action of a nilpotent group on its horofunction boundary has finite orbits
Group Theory
2011-04-12 v2 Metric Geometry
Abstract
We study the action of a nilpotent group G with finite generating set S on its horofunction boundary. We show that there is one finite orbit associated to each facet of the polytope obtained by projecting S into the infinite component of the abelianisation of G. We also prove that these are the only finite orbits of Busemann points. To finish off, we examine in detail the Heisenberg group with its usual generators.
Keywords
Cite
@article{arxiv.0806.0966,
title = {The action of a nilpotent group on its horofunction boundary has finite orbits},
author = {Cormac Walsh},
journal= {arXiv preprint arXiv:0806.0966},
year = {2011}
}
Comments
17 pages, 1 figure. Minor changes