Projections of polytopes on the plane and the generalized Baues problem

Athanasiadis, Christos

doi:10.1090/S0002-9939-00-05728-2

Projections of polytopes on the plane and the generalized Baues problem
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by Christos A. Athanasiadis PDF

Proc. Amer. Math. Soc. 129 (2001), 2103-2109 Request permission

Abstract:

Given an affine projection $\pi : P \to Q$ of a $d$-polytope $P$ onto a polygon $Q$, it is proved that the poset of proper polytopal subdivisions of $Q$ which are induced by $\pi$ has the homotopy type of a sphere of dimension $d-3$ if $\pi$ maps all vertices of $P$ into the boundary of $Q$. This result, originally conjectured by Reiner, is an analogue of a result of Billera, Kapranov and Sturmfels on cellular strings on polytopes and explains the significance of the interior point of $Q$ present in the counterexample to their generalized Baues conjecture, constructed by Rambau and Ziegler.

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