Cotangent spaces for higher Lie groupoids and applications

24.05.2024, 11:00 Uhr  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Stefano Ronchi (Göttingen)

In the same way Lie groupoids can encode local symmetries of a manifold, Lie 2-groupoids are a way to encode higher symmetries. After a short crash course on this topic, we present the construction of a cotangent space for Lie 2-groupoids analogous to the well known one for Lie groupoids. This turns out to have a canonical shifted symplectic structure (that is, symplectic up to homotopy) in the same way the cotangent groupoid is canonically a symplectic groupoid, and the tangent bundle of a manifold is canonically symplectic. This makes our cotangent space a good global model for a class of symplectic Q-manifolds that appear in some TQFTs. We will then discuss various applications, including a definition of hamiltonian actions of Lie 2-groupoids.
This talk is based on joint work in progress with Miquel Cueca and Chenchang Zhu.