Introduction to the h-principle

In 2019, I teach a graduate course about the h-principle in M2 AAG.

Main references are:

  • Eliashberg-Mishachev's book Introduction to the h-principle
  • Any lecture note from Vincent Borrelli.
  • Gromov's book Partial differential relations (hard)

There are lectures notes.

Student talks suggestions

In the following list, EM means Eliashberg-Mishchev's book. The first three items are directly in line with the lectures. The last two are much more ambitious, but giving an idea of how ideas from the lectures can be complemented with other ideas would already be nice.

  • Isosymplectic embeddings EM Thm 12.1.1. Holonomic approximation and symplectic geometry.
  • Holonomic approximation for microflexible relations EM chapter 13 (aim for Thm 13.4.1, bonus 16.1.2). Variation on proof of holonomic approximation.
  • First order differential operators EM Chap 20. Convex integration for operators like divergence.
  • René Thom and the h-principle Discuss how this paper proves existence of sphere eversion following ideas from Thom.
  • Convex integration ans PDEs Discuss this survey.
  • Positive isotopies of loose Legendrians Main result from this paper.
  • Legendriennes lâches et plastikstufe Theorem 1.1 from this paper.
  • Existence of contact structures in higher dimensions Discuss something of the main proof of this paper One more reasonnable goal could be explaining existence on closed 3-manifold from this point of view. See also this Bourbaki talk and references quoted at the end of introduction.
  • Topological characterization of Stein manifolds Thm 1.5 from this survey (see also Cieliebak and Eliashberg book if needed).

Differential topology

In 2016, I taught differential topology. Lectures notes (in french) can be found in pdf and web versions.

Exercices in "groupes et géométrie"

In 2012, I taught exercises sessions for Frédéric Paulin's M2 course.

Lecture notes are on Frédéric Paulin's website.

Below are the exercises.

updated on October 08 2019.