Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equipartitions of measures in $\mathbb{R}^4$   We prove that each measure $\mu$ in $R^4$ admits an equipartition by 4
hyperplanes, provided that it is symmetric with respect to a 2-dimensional,
affine subspace $L$ of $R^4$. Moreover we show, by computing the complete
obstruction in the relevant group of normal bordisms, that without the symmetry
condition, a naturally associated topological problem has a negative solution.
The computation is based on the Koschorke's exact singularity sequence and the
remarkable properties of the essentially unique, balanced binary Gray code in
dimension 4.

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The categories of this paper are: nlin
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The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: dg-ga