On flag spheres with few equators
Abstract
In this note we construct a flag simplicial 3-sphere with the following properties: - is not a suspension; - has no edge that can be contracted to obtain another flag sphere; - The only equators (induced subcomplexes which are spheres of codimension 1) of 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.
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