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Computational topology of equipartitions by hyperplanes
We compute a primary cohomological obstruction to the existence of an equipartition for $j$ mass distributions in $\mathbb{R}^d$ by two hyperplanes in the case $2d-3j = 1$. The central new result is that such an equipartition always exists if $d=6\cdot 2^k +2$ and $j=4\cdot 2^k+1$ which for $k=0$ reduces to …