The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes
نویسندگان
چکیده
We compute the Fadell-Husseini index of the dihedral group D8 = (Z2)2 ⋊ Z2 on S × S, that is, the kernel of the map in equivariant cohomology H ∗ D8 (pt,F2) −→ H ∗ D8 (Sd × Sd,F2). This establishes the complete cohomological lower bound for the two hyperplane case of Grünbaum’s 1960 mass partition problem: For which d and j can two hyperplanes be found that cut j arbitrary measures on R into four equal parts each?
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