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Summary: THE GENERALIZED BAUES PROBLEM FOR CYCLIC POLYTOPES II
CHRISTOS A. ATHANASIADIS, J ĻORG RAMBAU, AND FRANCISCO SANTOS
ABSTRACT. Given an affine surjection of polytopes : P Q, the Generalized
Baues Problem asks whether the poset of all proper polyhedral subdivisions of Q
which are induced by the map 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 : C(n, d ) C(n, d) for all 1 d < d < n.
1. INTRODUCTION
The Generalized Baues Problem, posed by Billera, Kapranov and Sturmfels [4],
is a question in combinatorial geometry and topology, motivated by the theory
of fiber polytopes [5] [18, Lecture 9]. Given an affine surjection of polytopes :
P Q, the problem asks to determine whether the Baues poset (P
Q) of all
proper polyhedral subdivisions of Q which are induced in a certain way by the
map , endowed with a standard topology [6], has the homotopy type of a sphere
of dimension dim(P) - dim(Q) - 1. We refer to [11] for a concise introduction and
[15] for a recent survey.
Although the Generalized Baues Problem is known to have a negative answer
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