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. 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.

References in corpus (2)

• Inscribing a regular crosspolytope
• Equipartition of a measure by $(Z_p{)}^k$-invariant fans

Cited by in corpus (1)

• Inscribing a regular octahedron into polytopes