The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes

Details The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes

2007-04-16

arxiv.org/abs/0704.1943v4

Mathematics

Algebraic Topology

new version revised according to referee's comments, 44 pages, many diagrams; a shorter version of this will appear in Topolog

Scientific paper

We compute the complete Fadell-Husseini index of the 8 element dihedral group D_8 acting on S^d \times S^d, both for F_2 and for integer coefficients. This establishes the complete goup cohomology lower bounds for the two hyperplane case of Gr"unbaum's 1960 mass partition problem: For which d and j can any j arbitrary measures be cut into four equal parts each by two suitably-chosen hyperplanes in R^d? In both cases, we find that the ideal bounds are not stronger than previously established bounds based on one of the maximal abelian subgroups of D_8.

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