Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instability of Reducible Critical Points of the Seiberg-Witten
  Functional   The Euler-Lagrange equations for the variational approach to the
Seiberg-Witten equations always admit reducible solutions. In this context, the
existence of unstable reducible solutions is achieved by assuming the existence
of a parallel spinor or the negativeness of a Perelman-Yamabe type of invariant
defined for a $\spinc$-structure.

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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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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: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci