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The Generalized Baues Problem for Cyclic Polytopes II

SC 98-43 Christos A. Athanasiadis, Jörg Rambau, Francisco Santos: The Generalized Baues Problem for Cyclic Polytopes II

Abstract: Given an affine surjection of polytopes $\pi: P \to Q$, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of Q which are induced by the map $\pi$has the homotopy type of a sphere. We extend earlier work of the last two authors on subdivisions of cyclic polytopes to give an affirmative answer to the problem for the natural surjections between cyclic polytopes $\pi: C(n,d) \to C(n,d)$ for all $1 \leq d < d < n$.
Keywords: Generalized Baues Problem, Polyhedral Subdivisions, Induced Subdivisions, Poset, Spherical, Cyclic Polytopes, Bistellar Operations
MSC: 52C22, 52B99