Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arithmetic topology in Ihara theory II: Milnor invariants, dilogarithmic
  Heisenberg coverings and triple power residue symbols   We introduce mod $l$ Milnor invariants of a Galois element associated to
Ihara's Galois representation on the pro-$l$ fundamental group of a punctured
projective line ($l$ being a prime number), as arithmetic analogues of Milnor
invariants of a pure braid. We then show that triple quadratic (resp. cubic)
residue symbols of primes in the rational (resp. Eisenstein) number field are
expressed by mod $2$ (resp. mod $3$) triple Milnor invariants of Frobenius
elements. For this, we introduce dilogarithmic mod $l$ Heisenberg ramified
covering ${\cal D}^{(l)}$ of $\mathbb{P}^1$, which may be regarded as a higher
analog of the dilogarithmic function, for the gerbe associated to the mod $l$
Heisenberg group, and we study the monodromy transformations of certain
functions on ${\cal D}^{(l)}$ along the pro-$l$ longitudes of Frobenius
elements for $l=2,3$.

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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: physics