Invariant vector fields and groupoids
arXiv:1307.7733
Abstract
We use the notion of isomorphism between two invariant vector fields to shed new light on the issue of linearization of an invariant vector field near a relative equilibrium. We argue that the notion is useful in understanding the passage from the space of invariant vector fields in a tube around a group orbit to the space invariant vector fields on a slice to the orbit. The notion comes from Hepworth's study of vector fields on stacks.
15 pages. Comments and corrections appreciated (v2): example added (v3): partially re-written in response to referees' comments. Accepted for publication in IMRN