Cross-index of free G-posets satisfies a sharp union bound xind(P) ≤ xind(A) + xind(B) + 1 for Z2 but only xind(P) ≤ xind(A) + 2(xind(B)+1) for other G, with arbitrarily large gap to the topological index.
The chromatic number of Kneser hypergraphs.Transactions of the American Mathematical Society, 298(1):359–370, 1986
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The mapping index through the lens of the cross-index
Cross-index of free G-posets satisfies a sharp union bound xind(P) ≤ xind(A) + xind(B) + 1 for Z2 but only xind(P) ≤ xind(A) + 2(xind(B)+1) for other G, with arbitrarily large gap to the topological index.