# University of Toronto's Symplectic Geometry Seminar

Monday February 21, 2005, 14:10--15:00

SS 5017A

## Chenchang Zhu

###
ETH Zurich

##
Stacky Lie groupoid and Lie theory

** Abstract: **
We all know that a Lie algebra has an associated simply connected Lie group
guaranteed by Lie's III theorem. However, Lie's III does not hold for a
geometrical generalization of Lie algebras---Lie algebroids (roughly, bundles
with fibres Lie algebras), namely, not any Lie algebroid has an associated Lie
groupoid. It turns out that if we enter the world of stacks and make sense what
a stacky groupoid is, this problem will naturally be solved! In fact, this
stacky groupoid "is" a 2-truncation of some simplicial manifold appearing in
Lie theory. Notations such as algebroids, groupoids, stacks, will be
explained.