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The Generalized Baues Problem for Cyclic Polytopes I.

Please always quote using this URN: urn:nbn:de:0297-zib-3579
  • 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.

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Author:Jörg Rambau, Francisco Santos
Document Type:ZIB-Report
Tag:Bistellar Operations; Cyclic Polytopes; Flip Defici; Generalized Baues Problem; Induced Subdivisions; Polyhedral Subdivisions; Poset; Spherical
MSC-Classification:52-XX CONVEX AND DISCRETE GEOMETRY / 52Bxx Polytopes and polyhedra / 52B99 None of the above, but in this section
52-XX CONVEX AND DISCRETE GEOMETRY / 52Cxx Discrete geometry / 52C22 Tilings in n dimensions [See also 05B45, 51M20]
Date of first Publication:1998/05/06
Series (Serial Number):ZIB-Report (SC-98-14)
Published in:Appeared in: European Journal of Combinatorics, 21(1), 2000, 65-83
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