On flag spheres with few equators
Lorenzo Venturello · arXiv (Cornell University) · 2022
In this note we construct a flag simplicial $3$-sphere $Δ$ with the following properties: - $Δ$ is not a suspension; - $Δ$ has no edge that can be contracted to obtain another flag sphere; - The only equators (induced subcomplexes which are spheres of codimension $1$) of $Δ$ are vertex links. Our construction has $12$ vertices, the minimum number of vertices such a simplicial complex can have. This answers a question posed by Chudnovsky and Nevo.