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arXiv · 1706.09539

Equivariant control data and neighborhood deformation retractions

Markus J. Pflaum·Graeme Wilkin
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Abstract

In this article we study Whitney (B) regular stratified spaces with the action of a compact Lie group $G$ which preserves the strata. We prove an equivariant submersion theorem and use it to show that such a $G$-stratified space carries a system of $G$-equivariant control data. As an application, we show that if $A \subset X$ is a closed $G$-stratified subspace which is a union of strata of $X$, then the inclusion $i : A \hookrightarrow X$ is a $G$-equivariant cofibration. In particular, this theorem applies whenever $X$ is a $G$-invariant analytic subspace of an analytic $G$-manifold $M$ and $A \hookrightarrow X$ is a closed $G$-invariant analytic subspace of $X$.

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Markus J. Pflaum, Graeme Wilkin. 2019-05-01. Equivariant control data and neighborhood deformation retractions. https://arxiv.org/abs/1706.09539

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