Cohomology in algebra, geometry, physicsand statistics

Formal integrability of geometric structures

A Γ-structure on a manifold is a maximal atlas whose changes of coordinates take values in a Lie pseudogroup Γ. Various geometric structures (e.g. symplectic, complex and contact structures) fit in this framework, but there is no general definition of almost Γ-structure (e.g. almost symplectic, almost complex and almost contact structures) in terms of Γ. In this talk we are going to fill this gap by introducing the general definition of an almost Γ-structure, and presenting a characterisation of its formal integrability. This will be obtained by introducing the concept of principal Pfaffian bundle. We will draw inspiration from the theory of PDEs, from Poisson geometry, as well as from similar results in the theory of G-structures, which we recover as particular cases. This is joint work with Marius Crainic.

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 ZOOM meeting shall be opened at 11.20 at

https://cesnet.zoom.us/j/99598413922?pwd=c2Y0TENuZHdDQ3hDWEkySFI3YWo3QT09

 

Meeting ID: 995 9841 3922

Passcode: cartan

and closed at 13.00