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arXiv · 0908.3097

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

R. N. Karasev
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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 consequences are: a result about inscribing skew crosspolytopes in hypersurfaces in $\mathbb R^{2^k}$, and a result about equipartition of a measures in $\mathbb R^{2^k}$ by $(Z_2)^{k+1}$-symmetric convex fans.

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R. N. Karasev. 2009-08-21. Knaster's problem for $(Z_2)^k$-symmetric subsets of the sphere $S^{2^k-1}$. https://doi.org/10.1007/s00454-009-9215-x

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