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Vector fields and flows on differentiable stacks

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Richard Hepworth

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.

Keywords:
Stacks, differentiable stacks, orbifolds, vector fields, flows

2000 MSC:
37C10, 14A20, 18D05

*Theory and Applications of Categories,*
Vol. 22, 2009,
No. 21, pp 542-587.

http://www.tac.mta.ca/tac/volumes/22/21/22-21.dvi

http://www.tac.mta.ca/tac/volumes/22/21/22-21.ps

http://www.tac.mta.ca/tac/volumes/22/21/22-21.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/21/22-21.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/21/22-21.ps

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/21/22-21.pdf

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