The higher Stasheff‐Tamari posets

This paper studies higher dimensional analogues of the Tamari lattice on triangulations of a convex n-gon, by placing a partial order on the triangulations of a cyclic d-polytope. Our principal results are that in dimension d≤3, these posets are lattices whose intervals have the homotopy type of a sphere or ball, and in dimension d≤5, all triangulations of a cyclic d-polytope are connected by bistellar operations.