Multiplicative Connections on Lie Groupoids

Luca Vitagliano (UNISA)

Sep 17. 2021, 11:00 — 12:00

We propose a new notion of multiplicative connection in the tangent bundle of a Lie groupoid. Multiplicative connections are a global version of Q-connections on a Q-manifold and their existence is obstructed by a cohomology class which a global counterpart of the Atiyah class of a Q-manifold (in the sense of Mehta, Stiénon and Xu). We discuss the Lie theory of multiplicative connections and present a bunch of examples. Our results can be easily generalized to multiplicative connections in VB-groupoids. This is the first step towards a theory of linear connections on differentiable stacks (joint work with: F. Pugliese and G. Sparano). 

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Geometry for Higher Spin Gravity: Conformal Structures, PDEs, and Q-manifolds (Thematic Programme)
Xavier Bekaert (U Tours)
Andreas Cap (U of Vienna)
Stefan Fredenhagen (U of Vienna)
Maxim Grigoriev (Lebedev Inst. & Lomonosov Moscow SU)
Alexei Kotov (U Hradec Králové)