2026/07/21 by Hehui Wu, Ningyuan Yang
#math.CO #math.AT
We prove Norine's conjecture: every red--blue edge-coloring of the \(n\)-dimensional hypercube \(Qn\), \(n≥2\), in which antipodal edges have opposite colors contains a monochromatic path joining some vertex to its antipode. From a hypothetical counterexample we construct an antipodally equivariant, augmentation-preserving chain map from the cellular chains of the cubical boundary of a cube to subdivision-invariant polyhedral chains on a sphere of one lower dimension. A purely algebraic chain-level Borsuk--Ulam obstruction rules out this map.