On the triangulation of stratified sets and singular varieties

Johnson, F. E. A.

doi:10.1090/S0002-9947-1983-0678354-5

On the triangulation of stratified sets and singular varieties
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Trans. Amer. Math. Soc. 275 (1983), 333-343 Request permission

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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Topolgische Begründung des Kalküls der abzählen Geometrie

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