2009
DOI: 10.1007/s00454-009-9215-x
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Knaster’s Problem for (Z 2) k -Symmetric Subsets of the Sphere $S^{2^{k}-1}$

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. As a consequence, we obtain a result about inscribing skew crosspolytopes in hypersurfaces in R 2 k and a result about equipartition of a measures in R 2 k by (Z 2 ) k+1 -symmetric convex fans.

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Cited by 4 publications
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“…One of the mechanisms for improving safety when performing work at a height is the use of certified, convenient means of individual and collective protection, as well as the use of various stationary systems that ensure the safety of the user when performing work at height [2][3][4][5]8].…”
Section: Introductionmentioning
confidence: 99%
“…One of the mechanisms for improving safety when performing work at a height is the use of certified, convenient means of individual and collective protection, as well as the use of various stationary systems that ensure the safety of the user when performing work at height [2][3][4][5]8].…”
Section: Introductionmentioning
confidence: 99%