Projecting \((N-1)\)-cycles to zero on hyperplanes in \(\mathbb R^{N+1}\). (Q1420507)

Consider a Lipschitz embedding \(M^{n-1}\to N^n\to\mathbb{R}^{n+1}\), where \(M\) is a homology \((n-1)\)-sphere and \(N\) is an ovaloid (that is, a \(C^2\)-hypersurface which bounds a compact, convex domain). Consider also a hyperplane \(P^n\subset\mathbb{R}^{n+1}\) and the orthogonal projection \(\pi :\mathbb{R}^{n+1}\to P\). \(M\) is said to project to zero on \(P\) whenever \(\pi_\ast (M) = 0\) in the space of \((n-1)\)-currents on \(P\). The main result (thm. 5.3) of the paper under review says that, in the situation described above, \(M\) cannot project to zero on \((n + 1)\) independent hyperplanes.