2017/06/29 by Markus J. Pflaum, Pflaum, Markus J., Graeme Wilkin +1 · 2 citations
Mathematics · #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.AT #math.DG #math.GT #math.SG
paper · pdf · doi:10.48550/arxiv.1706.09539
24 pages, to appear in Methods and Applications of Analysis
arxiv created 2019/05/01 · arxiv updated 2019/05/02
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 ⊂ 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.