Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Examples of Non-Busemann Horoballs   In the f.g. setting, we construct horoballs which are "not centered around a
geodesic" for generalized Heisenberg groups and all wreath products with an
infinite acting group. That is, we find are limits of balls -- called horoballs
-- which are not increasing unions of balls around points on a geodesic --
called Busemann horoballs. In the case of wreath products this follows from the
stronger fact that there exist disconnected horoballs; on the lamplighter group
we exhibit limits of Busemann horoballs which are not even coarsely connected.
In the case of generalized Heisenberg groups, we use a symmetry argument
instead; in fact for the $3$-dimensional Heisenberg group, at least under a
particular generating set, we show that all horoballs are connected.
  This note was written somewhat in isolation from the literature, in response
to a recent preprint of Epperlein and Meyerovitch asking for examples of
non-Busemann horoballs. It turns out that most of the results mentioned above
are known: The results about connectedness follow from known results about
almost convexity. The non-coarsely connected horoballs in the lamplighter
group, and connected non-Busemann horoballs in the Heisenberg group, may be new
statements, but here also we point out some strongly related literature.

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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: cs