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

DOI:
https://doi.org/10.1090/S0002-9939-00-05728-2

Published electronically:
November 21, 2000

MathSciNet review:
1825923

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Abstract | References | Similar Articles | Additional Information

Given an affine projection of a -polytope onto a polygon , it is proved that the poset of proper polytopal subdivisions of which are induced by has the homotopy type of a sphere of dimension if 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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Additional Information

**Christos A. Athanasiadis**

Affiliation:
Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden

Email:
athana@math.kth.se

DOI:
https://doi.org/10.1090/S0002-9939-00-05728-2

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