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

## Pavle V. M. Blagojević and Günter M. Ziegler – 2011

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.

Titel
The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes
Verfasser
Pavle V. M. Blagojević and Günter M. Ziegler
Datum
2011
Erschienen in
Topology and its Applications (Proc.\ ATA2010), volume 158, pages 1326-1351
Art
Text