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

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

2009-08-21

arxiv.org/abs/0908.3097v1

Discrete and Computational Geometry, 44:2, 2010, 429-438

Mathematics

Metric Geometry

Scientific paper

10.1007/s00454-009-9215-x

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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