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On Subdivision Posets of Cyclic Polytopes

✍ Scribed by Paul H. Edelman; Jörg Rambau; Victor Reiner

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
231 KB
Volume
21
Category
Article
ISSN
0195-6698

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✦ Synopsis

There are two related poset structures, the higher Stasheff-Tamari orders, on the set of all triangulations of the cyclic d polytope with n vertices. In this paper it is shown that both of them have the homotopy type of a sphere of dimension nd -3.

Moreover, we resolve positively a new special case of the Generalized Baues Problem: the Baues poset of all polytopal decompositions of a cyclic polytope of dimension d ≤ 3 has the homotopy type of a sphere of dimension nd -2.

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