Vector fields and flows on differentiable stacks

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)542-587
Number of pages46
JournalTheory and Applications of Categories
Volume22
Issue number21
Publication statusPublished - 2009

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Differentiable
Vector Field
Categorification
Morse Theory
Tangent Bundle
Orbifold
Differential Geometry
Lie Algebra
Existence and Uniqueness
Cell
Theorem

Cite this

Vector fields and flows on differentiable stacks. / Hepworth, Richard.

In: Theory and Applications of Categories, Vol. 22, No. 21, 2009, p. 542-587.

Research output: Contribution to journalArticle

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