2011/02/09 by Benjamin Braun, Braun, Benjamin, Matthew Zeckner +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.CO
paper · pdf · doi:10.48550/arxiv.1102.1984
15 pages, 1 figure
arxiv created 2011/02/09 · openalex publication_date 2011/02/09 · arxiv updated 2011/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 2003, A. Bjorner and M. de Longueville proved that the neighborhood complex of the stable Kneser graph SGn,k is homotopy equivalent to a k-sphere. Further, for n=2 they showed that the neighborhood complex deformation retracts to a subcomplex isomorphic to the associahedron. They went on to ask whether or not, for all n and k, the neighborhood complex of SGn,k contains as a deformation retract the boundary complex of a simplicial polytope. Our purpose is to give a positive answer to this question in the case k=2. We also find in this case that, after partially subdividing the neighborhood complex, the resulting complex deformation retracts onto a subcomplex arising as a polyhedral boundary sphere that is invariant under the action induced by the automorphism group of SGn,2.