Stratified vector fields on orbit spaces
Differential Geometry
2026-05-06 v1
Abstract
Using Morita type stratifications, we establish a one-to-one correspondence between geometric vector fields on a separated differentiable stack and stratified vector fields on its orbit space. This correspondence enables us to derive a stacky version of the generalized Gauss lemma and to prove a smooth version of Palais' covering isotopy theorem for a class of proper Lie groupoids, thereby extending the classical result for proper Lie group actions.
Cite
@article{arxiv.2605.03174,
title = {Stratified vector fields on orbit spaces},
author = {Mateus de Melo and Juan Sebastian Herrera-Carmona and Fabricio Valencia},
journal= {arXiv preprint arXiv:2605.03174},
year = {2026}
}
Comments
16 pages