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- W79491138 abstract "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." @default.
- W79491138 created "2016-06-24" @default.
- W79491138 creator A5058784973 @default.
- W79491138 date "2011-11-07" @default.
- W79491138 modified "2023-09-27" @default.
- W79491138 title "Equipartitions of measures by two hyperplanes" @default.
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