Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computational topology of equipartitions by hyperplanes   We compute a primary cohomological obstruction to the existence of an
equipartition for j mass distributions in R^d by two hyperplanes in the case
2d-3j = 1. The central new result is that such an equipartition always exists
if d=6 2^k +2 and j=4 2^k+1 which for k=0 reduces to the main result of the
paper P. Mani-Levitska et al., Topology and combinatorics of partitions of
masses by hyperplanes, Adv. Math. 207 (2006), 266-296. This is an example of a
genuine combinatorial geometric result which involves Z_4-torsion in an
essential way and cannot be obtained by the application of either
Stiefel-Whitney classes or cohomological index theories with Z_2 coefficients.
The method opens a possibility of developing an "effective primary obstruction
theory" based on $G$-manifold complexes, with applications in geometric
combinatorics, discrete and computational geometry, and computational algebraic
topology.

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The categories of this paper are: bayes-an
19
The categories of this paper are: eess
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph