René Thom and an anticipated h-principle - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2016

René Thom and an anticipated h-principle

Francois Laudenbach

Résumé

The first part of this article intends to present the role played by Thom in diffusing Smale’s ideas about immersion theory, at a time (1957) where some famous mathematicians were doubtful about them: it is clearly impossible to make the sphere inside out! Around a decade later, M. Gromov transformed Smale’s idea in what is now known as the h-principle. Here, the h stands for homotopy. Shortly after the astonishing discovery by Smale, Thom gave a conference in Lille (1959) announcing a theorem which would deserve to be named a homological h-principle. The aim of our second part is to comment about this theorem which was completely ignored by the topologists in Paris, but not in Leningrad. We explain Thom’s statement and answer the question whether it is true. The first idea is combinatorial. A beautiful subdivision of the standard simplex emerges from Thom’s article. We connect it with the jiggling technique introduced by W. Thurston in his seminal work on foliations.
Fichier principal
Vignette du fichier
Thom-anticipated2.pdf (1.69 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01494400 , version 1 (23-03-2017)
hal-01494400 , version 2 (08-04-2017)

Identifiants

Citer

Francois Laudenbach. René Thom and an anticipated h-principle. A tribute to René Thom, Sep 2016, Strasbourg, France. ⟨hal-01494400v1⟩
159 Consultations
400 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More