Stiefel manifolds and coloring the pentagon

We prove Csorbaʼs conjecture that the Lovász complex Hom ( C 5 , K n ) of graph multimorphisms from the 5-cycle C 5 to the complete graph K n is Z / 2 Z -equivariantly homeomorphic to the Stiefel manifold, V n − 1 , 2 , the space of (ordered) orthonormal 2-frames in R n − 1 .