Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dehn surgery, homology and hyperbolic volume   If a closed, orientable hyperbolic 3--manifold M has volume at most 1.22 then
H_1(M;Z_p) has dimension at most 2 for every prime p not 2 or 7, and H_1(M;Z_2)
and H_1(M;Z_7) have dimension at most 3. The proof combines several deep
results about hyperbolic 3--manifolds. The strategy is to compare the volume of
a tube about a shortest closed geodesic C in M with the volumes of tubes about
short closed geodesics in a sequence of hyperbolic manifolds obtained from M by
Dehn surgeries on C.

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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex