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

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} $, a n d a r e s u l t a b o u t e q u i p a r t i t i o n o f a m e a s u r e s i n$ \mathbb R^{2^k} $b y$ (Z_2)^{k+1}$-symmetric convex fans.

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

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

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Knaster's problem for (Z2)k(Z2​)k-symmetric subsets of the sphere S2k−1S2k−1

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Knaster's problem for (Z2)k(Z2​)k-symmetric subsets of the sphere S2k−1S2k−1

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

讲解博客

AI智能校验

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

讲解博客

AI智能校验