Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The action of a nilpotent group on its horofunction boundary has finite
  orbits   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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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: cs