Sep 20 – 22, 2023
Le Bois-Marie
Europe/Paris timezone

Doors opened by Thom in Morse theory and towards the h-principle

Sep 20, 2023, 12:10 PM
Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Centre de conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette


Prof. Emmanuel Giroux (CNRS et ENS)


We will review the content and the influence of two papers by R. Thom. The first is his 1949 note "sur une partition en cellules associée à une fonction sur une variété" where he exhibits the cell decomposition provided by any gradient of a Morse function ; we will also discuss the two unpublished manuscripts dated 1957 where Thom applies Morse Theory to analyze the topology of complex affine algebraic/analytic manifolds. The second article is the 1959 paper "remarques sur les problèmes comportant des inéquations différentielles globales" where Thom scatters seeds for the general study of open differential relations, a theme that Gromov will later embrace in the vast theory of the h-principle.

Presentation materials