Methods and Applications of Analysis
Volume 26 (2019)
In Memory of Professor John N. Mather: Part 3 of 3
Guest Editors: Sen Hu, University of Science and Technology, China; Stanisław Janeczko, Polish Academy of Sciences, Poland; Stephen S.-T. Yau, Tsinghua University, China; and Huaiqing Zuo, Tsinghua University, China.
Equivariant control data and neighborhood deformation retractions
Pages: 13 – 36
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 $X$.
equivariant control data, equivariant Whitney stratification, equivariant tubular neighbourhood, equivariant cofibration
2010 Mathematics Subject Classification
32C25, 57N80, 57R99
Received 8 August 2018
Accepted 29 January 2019
Published 14 November 2019