Séminaire Physique mathématique ICJ

Shifted contact structures on differentiable stacks

by Prof. Luca Vitagliano

Fokko du Cloux (Bâtiment Braconnier)

Fokko du Cloux

Bâtiment Braconnier


the main aim of this talk is proposing a definition of +1-shifted contact structure on a differentiable stack thus laying the foundations of +1-shifted contact geometry. As a side result I will show that the kernel of a multiplicative 1-form on a Lie groupoid (might not exist as a vector bundle of Lie groupoids but) it always exists as a vector bundle of differentiable stacks and it carries a stacky version of the curvature of a distribution. Prequantum bundles over +1-shifted symplectic groupoids provide examples of +1-shifted contact structures. Time permitting, I will also discuss 0-shifted contact structures which, in some aspects, are surprisingly more complicated than +1-shifted ones. This is joint work with A. Maglio and A. Tortorella.