ON SUBDIVISION POSETS OF CYCLIC POLYTOPES

PAUL H. EDELMAN JÖRG RAMBAU AND VICTOR REINER

Abstract. There are two related poset structures, the higher Stasheff-Tamari orders, on the set of all triangulations of the cyclic d polytope with n vertices. In this paper it is shown that both of them have the homotopy type of a sphere of dimension n − d − 3.

Moreover, we resolve positively a new special case of the Generalized Baues Problem: The Baues poset of all polytopal decompositions of a cyclic polytope of dimension d ≤ 3 has the homotopy type of a sphere of dimension n − d − 2.