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

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

2008-06-05

arxiv.org/abs/0806.0966v2

Groups, Geometry, and Dynamics. 5 (2011) 189-206

Mathematics

Group Theory

17 pages, 1 figure. Minor changes

Scientific paper

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.

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