Proceedings of the American Mathematical Society

Author(s): Christos A. Athanasiadis
Journal: Proc. Amer. Math. Soc. 129 (2001), 2103-2109.
MSC (2000): Primary 52B11; Secondary 06A07, 55P15
Posted: November 21, 2000
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Given an affine projection $\pi: P \to Q$ of a

-polytope

onto a polygon

, it is proved that the poset of proper polytopal subdivisions of

which are induced by $\pi$ has the homotopy type of a sphere of dimension

if $\pi$ maps all vertices of

into the boundary of

. 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

present in the counterexample to their generalized Baues conjecture, constructed by Rambau and Ziegler.

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Christos A. Athanasiadis
Affiliation: Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Email: athana@math.kth.se

DOI: 10.1090/S0002-9939-00-05728-2
PII: S 0002-9939(00)05728-2
Received by editor(s): September 29, 1999
Received by editor(s) in revised form: October 22, 1999
Posted: November 21, 2000
Additional Notes: The author's research was supported by the Göran Gustafsson Foundation at the Royal Institute of Technology, Stockholm, Sweden.
Communicated by: John R. Stembridge
Copyright of article: Copyright 2000, American Mathematical Society

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