3 research outputs found

    Knaster's problem for (Z2)k(Z_2)^k-symmetric subsets of the sphere S2k1S^{2^k-1}

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    We prove a Knaster-type result for orbits of the group (Z2)k(Z_2)^k in S2k1S^{2^k-1}, calculating the Euler class obstruction. Among the consequences are: a result about inscribing skew crosspolytopes in hypersurfaces in R2k\mathbb R^{2^k}, and a result about equipartition of a measures in R2k\mathbb R^{2^k} by (Z2)k+1(Z_2)^{k+1}-symmetric convex fans
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