Collapsible polyhedra and median spaces

van de Vel, M.

doi:10.1090/S0002-9939-98-04413-X

Collapsible polyhedra and median spaces
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by M. van de Vel

Proc. Amer. Math. Soc. 126 (1998), 2811-2818

DOI: https://doi.org/10.1090/S0002-9939-98-04413-X

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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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