Kalai's 3^d conjecture

ID: kalai-s-3-d-conjecture

Kalai's 3-dimensional conjecture, proposed by Gil Kalai, pertains to the geometry of convex polytopes. The conjecture specifically addresses the conditions under which a simplicial complex can be realized as the nerve of a covering by open sets in a topological space. More concretely, it asserts that any simplicial complex that has a specific homotopy type will have a realization in a three-dimensional space.

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