Vector Fields and Flows on Differentiable Stacks
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2008
- DOI:
- 10.48550/arXiv.0810.0979
- arXiv:
- arXiv:0810.0979
- Bibcode:
- 2008arXiv0810.0979H
- Keywords:
-
- Mathematics - Differential Geometry;
- Mathematics - Category Theory;
- 37C10;
- 14A20;
- 18D05
- E-Print:
- 41 pages