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A triangulation criterion
Published online by Cambridge University Press: 26 February 2010
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The aim of this paper is to prove the following
Theorem A. Let K be an ordered, locally finite, simplicial complex, considered as a category, let L be a subcomplex, and let F : K → PL be a functor. Then
(i) the geometric realisation 〈F〉 of F has a natural PL structure in which 〈F|L〉 is a subpolyhedron, and, in particular,
(ii) 〈F〉 admits a triangulation by a locally finite simplicial complex in which 〈F|L〉 is triangulated as a subcomplex.
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- Copyright © University College London 1978
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