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Collapsible polyhedra and median spaces

Author: M. van de Vel
Journal: Proc. Amer. Math. Soc. 126 (1998), 2811-2818
MSC (1991): Primary 57Q99, 52A01; Secondary 05C99
MathSciNet review: 1452832
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Abstract: It is shown that a collapsible, compact, connected, simplicial polyhedron admits a cubical subdivision and a median convexity, such that all cubes are convex subspaces with a convexity of subcubes. Conversely, a compact, connected, cubical polyhedron with a convexity as described admits a collapsible simplicial subdivision. Such a convexity, when it exists, is uniquely determined by the corresponding cubical presentation. Some related open problems have been formulated.

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Additional Information

M. van de Vel
Affiliation: Fakulteit Wiskunde en Informatika, Vrije Universiteit, NL-1081 HV Amsterdam, the Netherlands

Keywords: Collapsible polyhedron, convex structure, cubical complex, gate map, injective metric, median graph, median operator, simplicial complex
Received by editor(s): February 22, 1996
Received by editor(s) in revised form: February 5, 1997
Dedicated: This paper is dedicated to the memory of my son Wouter, 1974–1993
Communicated by: Christopher Croke
Article copyright: © Copyright 1998 American Mathematical Society