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On flag spheres with few equators
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In this note we construct a flag simplicial $3$-sphere $\Delta$ with the following properties: - $\Delta$ is not a suspension; - $\Delta$ has no edge that can be contracted to obtain another flag sphere; - The only equators (induced subcomplexes which are spheres of codimension $1$) of $\Delta$ 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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Cited by 1 Pith paper
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Lower bounds on the $g$-numbers of spheres without large missing faces
Simplicial spheres without large missing faces satisfy g-number lower bounds in terms of graph independence numbers, including g2 ≥ (1/2 − δ(d))f0 for flag spheres with δ(d) → 0 as d → ∞.
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