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arXiv · 2605.03174

Stratified vector fields on orbit spaces

Mateus de Melo·Juan Sebastian Herrera-Carmona·Fabricio Valencia
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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.

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Mateus de Melo, Juan Sebastian Herrera-Carmona, Fabricio Valencia. 2026-05-04. Stratified vector fields on orbit spaces. https://arxiv.org/abs/2605.03174

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