Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T22:12:15.777Z Has data issue: false hasContentIssue false
  • English
  • Français

On the presentation of stratified sets and singular varieties

Part of: General theory of differentiable manifolds

Published online by Cambridge University Press:  26 February 2010

F. E. A. Johnson
F. E. A. Johnson
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E 6BT
Get access

Extract

The aim of this paper is to give a clear statement, and, I hope, a reasonably clear proof, of a theorem of Thorn, which occurs in his important and difficult paper “Ensembles et morphismes stratifiés” [10]. The theorem to which I refer is Théorème 1.D.1 of [10]. “Tout espace stratifié compact admet une présentation associée aux applications kYX données”. At least, I think that the theorem herein described is equivalent to the above, but I could not swear to it. The main difficulty is that, despite strenuous efforts on my part, I have always found it easier to rig up my own system of definitions than to work within the framework suggested by Thorn. However, the two accounts clearly say the same sort of thing. In particular, §1 of the present paper is closely related to, and heavily influenced by, the material on page 250 of [10].

MSC classification

Secondary: 58A35: Stratified sets
Type
Research Article
Information
Mathematika , Volume 29 , Issue 1 , June 1982 , pp. 135 - 170
Copyright
Copyright © University College London 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Cerf, J.. Topologie de certains espaces de plongements. Bull Soc. Math. France, 89 (1961), 227–380.Google Scholar
2.Douady, A. et Herault, L.. Arrondissement des variètès á coins. Appendix to “Corners and Arithmetic Groups”, by A. Borel and J. P. Serre. Comment. Math. Helv., 48 (1973), 436–491.Google Scholar
3.Johnson, F. E. A.. Triangulation of stratified sets. (Thesis, University of Liverpool, 1972).Google Scholar
1.Johnson, F. E. A.. A triangulation criterion. Mathematika, 25 (1978), 110–114.Google Scholar
5.Johnson, F. E. A.. On the triangulation of smooth fibre bundles. To appear in Fund. Math.Google Scholar
6.Johnson, F. E. A.. On the triangulation of stratified sets and singular varieties. To appear in Trans. Amer. Math. Soc.Google Scholar
7.Malgrange, B.. Ideals of differential functions (Tata Institute for Fundamental Research, 1964).Google Scholar
8.Mather, J.. Notes on topological stability (Harvard University, 1970).Google Scholar
9.Stravinsky, I.. Apropos of Le Sacre. Stravinsky conducts Stravinsky. La Sacre du Printemps. C.B.S. Recording 72054 (1960).Google Scholar
10.Thorn, R.. Ensembles et morphismes stratifiès. Bull. Amer. Math. Soc., 75 (1969), 240–284.Google Scholar