math_groups_discgeom

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.

TitelThe ideal-valued index for a dihedral group action, and mass partition by two hyperplanes
VerfasserPavle V. M. Blagojević and Günter M. Ziegler
Datum2011
Quelle/n
Erschienen inTopology and its Applications (Proc.\ ATA2010), volume 158, pages 1326-1351
ArtText