Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heegaard splittings of graph manifolds   Let M be a totally orientable graph manifold with characteristic submanifold
T and let M = V cup_S W be a Heegaard splitting. We prove that S is standard.
In particular, S is the amalgamation of strongly irreducible Heegaard
splittings. The splitting surfaces S_i of these strongly irreducible Heegaard
splittings have the property that for each vertex manifold N of M, S_i cap N is
either horizontal, pseudohorizontal, vertical or pseudovertical.

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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th