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The generalized Baues problem for cyclic polytopes. II. (English) Zbl 1009.52023

A general Baues problem is the question whether for a given surjection \(\pi:P\to Q\) of convex polytopes, the poset of all proper polyhedral subdivisions of \(Q\), induced by \(\pi\), is a homotopy sphere. The main result is an affirmative answer to the Baues problem if \(P\) and \(Q\) are assumed to be cyclic polytopes and \(\pi\) is a naturally defined map. The main tool is the so called “sliding” technique that has been introduced and previously used by the authors in other Baues type problems [see Eur. J. Comb. 21, 65-83 (2000; Zbl 0951.52011)].

MSC:

52B11 \(n\)-dimensional polytopes

Citations:

Zbl 0951.52011
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