Publication Date:
2014-11-10
Description:
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.
Keywords:
ddc:000
Language:
English
Type:
reportzib
,
doc-type:preprint
Format:
application/postscript
Format:
application/pdf
