Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A divergent horocycle in the horofunction compactification of the
  Teichm\"uller metric   We give an example of a horocycle in the Teichm\"uller space of the
five-times-punctured sphere that does not converge in the Gardiner--Masur
compactification, or equivalently in the horofunction compactification of the
Teichm\"uller metric. As an intermediate step, we exhibit a simple closed curve
whose extremal length is periodic but not constant along the horocycle. The
example lifts to any Teichm\"uller space of complex dimension greater than one
via covering constructions.

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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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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: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph