On the triangulation of stratified sets and singular varieties
Open Access
- 1 January 1983
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 275 (1) , 333-343
- https://doi.org/10.1090/s0002-9947-1983-0678354-5
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.Keywords
This publication has 15 references indexed in Scilit:
- On the presentation of stratified sets and singular varietiesMathematika, 1982
- A triangulation criterionMathematika, 1978
- Corners and arithmetic groupsCommentarii Mathematici Helvetici, 1973
- Ensembles et morphismes stratifiésBulletin of the American Mathematical Society, 1969
- Tangents to an Analytic VarietyAnnals of Mathematics, 1965
- The triangulability of the orbit space of a differentiable transformation groupBulletin of the American Mathematical Society, 1963
- On C 1 -ComplexesAnnals of Mathematics, 1940
- On Analytical ComplexesTransactions of the American Mathematical Society, 1933
- On the Covering of Analytic Loci by ComplexesTransactions of the American Mathematical Society, 1932
- Topologische Begründung des Kalküls der abzählenden GeometrieMathematische Annalen, 1930