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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Projections of polytopes on the plane and the generalized Baues problem


Author: Christos A. Athanasiadis
Journal: Proc. Amer. Math. Soc. 129 (2001), 2103-2109
MSC (2000): Primary 52B11; Secondary 06A07, 55P15
Published electronically: November 21, 2000
MathSciNet review: 1825923
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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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Additional Information

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

DOI: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2000 American Mathematical Society