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A triangulation criterion

Published online by Cambridge University Press:  26 February 2010

F. E. A. Johnson
F. E. A. Johnson
Affiliation:
Department of Mathematics, University College, London.
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Extract

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.

Type
Research Article
Information
Mathematika , Volume 25 , Issue 1 , June 1978 , pp. 110 - 114
Copyright
Copyright © University College London 1978

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References

1.Curtis, E. B.. “Simplicial homotopy theory”, Advances in Mathematics, 6 (1971), 107–209.CrossRefGoogle Scholar
2.Hudson, J. F. P.. Piecewise linear topology (Benjamin, 1969).Google Scholar
3.Gabriel, P. and Zisman, M.. “Calculus of fractions and homotopy theory”, Ergebnisse der Math. (Springer-Verlag, 1967).Google Scholar
4.Johnson, F. E. A.. Triangulation of stratified sets. Thesis (University of Liverpool, 1972).Google Scholar
5.Johnson, F. E. A.. “Triangulation of stratified sets and singular varieties” (to appear).Google Scholar
6.Segal, G. B.. “Classifying spaces and spectral sequences”, I.H.E.S. Publ. Math., 34 (1968), 105–112.CrossRefGoogle Scholar
7.Thom, R.. “Ensembles et Morphismes Stratifies”, Bull. Amer. Math. Soc, 75 (1969), 240–284.CrossRefGoogle Scholar