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Collapsible polyhedra and median spaces
Author(s):
M.
van de Vel
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2811-2818.
MSC (1991):
Primary 57Q99, 52A01;
Secondary 05C99
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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
Email:
marcel@cs.vu.nl
DOI:
10.1090/S0002-9939-98-04413-X
PII:
S 0002-9939(98)04413-X
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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