Lauran Toussaint

Title: H-principles and Haefliger structures.

Abstract: The h-principle is a collection of techniques to study the
space of solutions of a partial differential relation. On open
manifolds the existence of many geometric structures, for example
symplectic structures, can be proven using these methods. On closed
manifolds the situation is more complicated. However, Laudenbach and
Meigniez showed that for several geometries it is still possible to
obtain a singular solution, called a Haefliger structure.  In this
talk I discuss joint work with A. del Pino extending this result to
any (open, Diff-invariant) partial differential relation. The first
part of the talk consists of an introduction to the h-principle and
Haefliger structures.  Then I will apply these ideas to construct
folded symplectic structures, recovering a result by Cannas da Silva.