Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bianchi's additional symmetries   In a 2012 note in Comptes Rendus Math{\'e}matique, the author did try to
answer a question of Jean-Pierre Serre; it has recently been announced that the
scope of that answer needs an adjustment, and the details of this adjustment
are given in the present paper. The original question is the following.
Consider the ring of integers O in an imaginary quadratic number field, and the
Borel-Serre compactification of the quotient of hyperbolic 3-space by SL 2 (O).
Consider the map $\alpha$ induced on homology when attaching the boundary into
the Borel-Serre compactification. How can one determine the kernel of $\alpha$
(in degree 1) ? Serre used a global topological argument and obtained the rank
of the kernel of $\alpha$. He added the question what submodule precisely this
kernel is.

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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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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: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex