Knaster's problem for $Z 2^k$-symmetric subsets of the sphere $S^{2^k-1}$ - Mathematics > Metric GeometryReport as inadecuate




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Abstract: We prove a Knaster-type result for orbits of the group $Z 2^k$ in$S^{2^k-1}$, calculating the Euler class obstruction. Among the consequencesare: a result about inscribing skew crosspolytopes in hypersurfaces in $\mathbbR^{2^k}$, and a result about equipartition of a measures in $\mathbb R^{2^k}$by $Z 2^{k+1}$-symmetric convex fans.



Author: R.N. Karasev

Source: https://arxiv.org/







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