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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On the triangulation of stratified sets and singular varieties


Author: F. E. A. Johnson
Journal: Trans. Amer. Math. Soc. 275 (1983), 333-343
MSC: Primary 58A35; Secondary 32B25, 54E60, 57R05
MathSciNet review: 678354
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Abstract: We show that every compact stratified set in the sense of Thom can be triangulated as a simplicial complex. The proof uses that author's description of a stratified set as the geometric realisation of a certain type of diagram of smooth fibre bundles and smooth imbeddings, and the triangulability of smooth fibre bundles.

As a consequence, we obtain proofs of the classical triangulation theorems for analytic and subanalytic sets, and a correct proof of Yang's theorem that the orbit space of a smooth compact transformation group is triangulable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0678354-5
PII: S 0002-9947(1983)0678354-5
Article copyright: © Copyright 1983 American Mathematical Society