Vector Fields and Flows on Differentiable Stacks

Details Vector Fields and Flows on Differentiable Stacks Vector Fields and Flows on Differentiable Stacks

2008-10-06

arxiv.org/abs/0810.0979v1

Theory Appl. Categ. 22 (2009), 542-587

Mathematics

Differential Geometry

41 pages

Scientific paper

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.

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