Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Incompressible surfaces, hyperbolic volume, Heegaard genus and homology   We show that if M is a complete, finite-volume, hyperbolic 3-manifold having
exactly one cusp, and if H_1(M;Z_2) has dimension at least 6, then M has volume
greater than 5.06. We also show that if M is a closed, orientable hyperbolic
3-manifold such that H_1(M;Z_2) has dimension at least 4, and if the image of
the cup product map in H^2(M;Z_2) has dimension at most 1, then M has volume
greater than 3.08. The proofs of these geometric results involve new
topological results relating the Heegaard genus of a closed Haken manifold M to
the Euler characteristic of the kishkes (i.e guts) of the complement of an
incompressible surface in M.

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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin