Vector Fields and Flows on Differentiable Stacks
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Vector Fields and Flows on Differentiable Stacks. / A. Hepworth, Richard.
I: Theory and Applications of Categories, Bind 22, 2009, s. 542-587.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Vector Fields and Flows on Differentiable Stacks
AU - A. Hepworth, Richard
N1 - Keywords: math.DG; math.CT; 37C10, 14A20, 18D05
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
M3 - Journal article
VL - 22
SP - 542
EP - 587
JO - Theory and Applications of Categories
JF - Theory and Applications of Categories
SN - 1201-561X
ER -
ID: 21543300