Stiefel Manifolds and Coloring the Pentagon
Abstract
We prove Csorba's conjecture that the Lov\'asz complex Hom(C5,Kn) of graph multimorphisms from the 5-cycle C5 to the complete graph Kn is Z/2Z-equivariantly homeomorphic to the Stiefel manifold, V(n-1,2), the space of (ordered) orthonormal 2-frames in Rn-1. The equivariant piecewise-linear topology that we need is developed along the way.
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