Geodesic
The action of a nilpotent group on its horofunction boundary has finite orbits
Cormac Walsh1
1Ecole Polytechnique, Palaiseau, France
Groups, geometry, and dynamics, Tome 5 (2011) no. 1, pp. 189-206

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DOI

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 torsion-free 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.
DOI : 10.4171/ggd/122
Classification : 20-XX, 00-XX
Mots-clés : Group action, horoball, max-plus algebra, metric boundary, Busemann function

Cormac Walsh  1

1 Ecole Polytechnique, Palaiseau, France 
Cormac Walsh. The action of a nilpotent group on its horofunction boundary has finite orbits. Groups, geometry, and dynamics, Tome 5 (2011) no. 1, pp. 189-206. doi: 10.4171/ggd/122
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     title = {The action of a nilpotent group on its horofunction boundary has finite orbits},
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     year = {2011},
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     number = {1},
     doi = {10.4171/ggd/122},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/122/}
}
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