TY - GEN A1 - Athanasiadis, Christos A. A1 - Rambau, Jörg A1 - Santos, Francisco T1 - The Generalized Baues Problem for Cyclic Polytopes II N2 - 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 $1 \leq d < d' < n$. T3 - ZIB-Report - SC-98-43 KW - Generalized Baues Problem KW - Polyhedral Subdivisions KW - Induced Subdivisions KW - Poset KW - Spherical KW - Cyclic Polytopes KW - Bistellar Operations Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3862 ER - TY - GEN A1 - Rambau, Jörg A1 - Santos, Francisco T1 - The Generalized Baues Problem for Cyclic Polytopes I. N2 - The Generalized Baues Problem asks whether for a given point configuration the order complex of all its proper polyhedral subdivisions, partially ordered by refinement, is homotopy equivalent to a sphere. In this paper, an affirmative answer is given for the vertex sets of cyclic polytopes in all dimensions. This yields the first non-trivial class of point configurations with neither a bound on the dimension, the codimension, nor the number of vertice for which this is known to be true. Moreover, it is shown that all triangulations of cyclic polytopes are lifting triangulations. This contrasts the fact that in general there are many non-regular triangulations of cyclic polytopes. Beyond this, we find triangulations of $C(11,5)$ with flip deficiency. This proves---among other things---that there are triangulations of cyclic polytopes that are non-regular for every choice of points on the moment curve. T3 - ZIB-Report - SC-98-14 KW - Generalized Baues Problem KW - Polyhedral Subdivisions KW - Induced Subdivisions KW - Poset KW - Spherical KW - Cyclic Polytopes KW - Bistellar Operations KW - Flip Defici Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3579 ER -