Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthotree, orthoshapes and ortho-integral surfaces   This paper describes a tree structure on the set of orthogeodesics leading to
a combinatorial proof of Basmajian's identity in the case of surfaces. It is
motivated by a number theoretic application of Bridgeman's identity, the
combinatorial proof of McShane's identity by Bowditch and its generalized
version by Labourie and Tan. We also introduce the notion of orthoshapes with
associated identity relations and indicate connections to length equivalent
orthogeodesics and a type of Cayley-Menger determinant. As another application,
dilogarithm identities following from Bridgeman's identity are computed
recursively and their terms are indexed by the Farey sequence.

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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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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: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin