Abstract
In 1995, Jockusch constructed an infinite family of centrally symmetric 3-dimensional simplicial spheres that are cs-2-neighborly. Here we generalize his construction and show that for all d≥3 and n≥d+1, there exists a centrally symmetric d-dimensional simplicial sphere with 2n vertices that is cs-⌈d/2⌉-neighborly. This result combined with work of Adin and Stanley completely resolves the upper bound problem for centrally symmetric simplicial spheres.
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