Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Effective Compactness Theorem for Coxeter Groups   Through highly non-constructive methods, works by Bestvina, Culler, Feighn,
Morgan, Paulin, Rips, Shalen, and Thurston show that if a finitely presented
group does not split over a virtually solvable subgroup, then the space of its
discrete and faithful actions on hyperbolic n-space, modulo conjugation, is
compact for all dimensions. Although this implies that the space of hyperbolic
structures of such groups has finite diameter, the known methods do not give an
explicit bound. We establish such a bound for Coxeter groups. We find that
either the group splits over a virtually solvable subgroup or there is a
constant C and a point in hyperbolic n-space that is moved no more than C by
any generator. The constant C depends only on the number of generators of the
group, and is independent of the relators.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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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: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph