Lie theory of Lie algebroids via higher structures in differentiable geometry
Speaker:
Chenchang Zhu, Georg-August-Universität Göttingen and University of Goettingen
Date and Time:
Monday, May 14, 2007 - 2:30pm to 3:30pm
Location:
Fields Institute, Room 230
Abstract:
Higher structures such as differentiable stacks, simplicial objects, Lie groupoids, gerbes have been recently introduced in differential geometry. They are useful, for example, to integrate Lie algebroids. Lie algebroids are a mixture of Lie algebras and manifolds, or it could be understood as a degree-1 super-manifold with a degree-1 vector field Q with Q2 = 0. Unlike a (finite dimensional) Lie algebra which always has a (simply connected) Lie group corresponding to, a Lie algebroid may not have a corresponding Lie groupoid. But there is a one-to-one correspondence between Lie algebroids and stacky Lie groupoids (or Lie 2-groupoids). Lie’s second theorem also holds for these universal objects