Thierry Robart (joint work with Niky Kamran)
At the conclusion of a decade-long collaborative effort we published [*] in 2004 the following existence theorem for Lie pseudogroups of infinite type.
Each local Lie pseudogroup of analytic transformations admits an analytic manifold structure. That latter is moreover compatible for the operations of its isotropy subgroup.
Our proof is based on the existence of a canonical chart of the second kind.
This lecture will be devoted to surveying the main steps of our construction.
[*] N. Kamran, T. Robart, An Infinite-Dimensional Manifold Structure for Analytic Lie Pseudogroups of Infinite Type, IMRN 2004, no. 34, p. 1761-1783.