Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Balanced presentations of the trivial group on two generators and the
  Andrews-Curtis conjecture   The Andrews-Curtis conjecture states that every balanced presentation of the
trivial group can be reduced to the standard one by a sequence of the
elementary Nielsen transformations and conjugations. In this paper we describe
all balanced presentations of the trivial group on two generators and with the
total length of relators <= 12. We show that all these presentations satisfy
the Andrews-Curtis conjecture.

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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: physics