Equipartitions of measures by two hyperplanes

Details Equipartitions of measures by two hyperplanes Equipartitions of measures by two hyperplanes

2011-11-07

arxiv.org/abs/1111.1608v1

Mathematics

Combinatorics

Scientific paper

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.

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