Abstract
This paper introduces the notions of vector field and flow on a general differentiable stack. Our main theorem states that the flow of a vector field on a compact proper differentiable stack exists and is unique up to a uniquely determined 2-cell. This extends the usual result on the existence and uniqueness of flows on a manifold as well as the author's existing results for orbifolds. It sets the scene for a discussion of Morse Theory on a general proper stack and also paves the way for the categorification of other key aspects of differential geometry such as the tangent bundle and the Lie algebra of vector fields.
| Original language | English |
|---|---|
| Journal | Theory and Applications of Categories |
| Volume | 22 |
| Pages (from-to) | 542-587 |
| ISSN | 1201-561X |
| Publication status | Published - 2009 |