Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On \pi-surfaces of four-dimensional parallelohedra   We show that every four-dimensional parallelohedron P satisfies a recently
found condition of Garber, Gavrilyuk & Magazinov sufficient for the Voronoi
conjecture being true for P. Namely we show that for every four-dimensional
parallelohedron P the group of rational first homologies of its \pi-surface is
generated by half-belt cycles.

7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: adap-org