Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On typical leaves of a measured foliated 2-complex of thin type   It is known that all but finitely many leaves of a measured foliated
2-complex of thin type are quasi-isometric to an infinite tree with at most two
topological ends. We show that if the foliation is cooriented, and the
associated R-tree is self-similar, then a typical leaf has exactly one
topological end. We also construct the first example of a foliated 2-complex of
thin type whose typical leaf has exactly two topological ends. `Typical' means
that the property holds with probability one in a natural sense.

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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an