Vector Fields and Flows on Differentiable Stacks

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

SN - 1201-561X

VL - 22

SP - 542

EP - 587

JO - Theory and Applications of Categories

JF - Theory and Applications of Categories

ER -