Stiefel Manifolds and Coloring the Pentagon

2013/02/12 by James Dover, Dover, James, Murad Özaydın +1
Computer Science · Mathematics · #05E18 #57Q15 #57Q40 #57Q91 #57S25 #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1302.2831

openalex publication_date 2013/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove Csorba's conjecture that the Lovász complex Hom(C₅,K_n) of graph multimorphisms from the 5-cycle C₅ to the complete graph K_n is Z/2Z-equivariantly homeomorphic to the Stiefel manifold, V(n-1,2), the space of (ordered) orthonormal 2-frames in R^n-1. The equivariant piecewise-linear topology that we need is developed along the way.

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