JournalsggdVol. 5, No. 1pp. 189–206

The action of a nilpotent group on its horofunction boundary has finite orbits

  • Cormac Walsh

    Ecole Polytechnique, Palaiseau, France
The action of a nilpotent group on its horofunction boundary has finite orbits cover

Abstract

We study the action of a nilpotent group GG with finite generating set SS on its horofunction boundary. We show that there is one finite orbit associated to each facet of the polytope obtained by projecting SS into the torsion-free component of the abelianisation of GG. 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.

Cite this article

Cormac Walsh, The action of a nilpotent group on its horofunction boundary has finite orbits. Groups Geom. Dyn. 5 (2011), no. 1, pp. 189–206

DOI 10.4171/GGD/122