Léo Brunswic

Traditionally, a $(G,X)$-manifold is a manifold locally modeled on X with change of charts in $G$, some Lie group acting analytically on $X$. In most common examples, $X$ is a spaceform and $G$ is its group of isometries. The strength of the theory of $(G,X)$-manifold comes from the developing Theorem that allows to compare a manifold $M$ to the model space and in many instance construct a natural identification $\Omega/\Gamma \simeq  M$ with $\Omega$ a domain of $X$ with $\Gamma$ a group acting on $X$ preserving $\Omega$. The study of such manifolds with singularities is common with a notion of singularity depending on context. We present a possible starting point for a theory unifying the notions of singularities, we prove many general properties allowing to manipulate singular (G,X)-manifolds with peace of mind. We also provide a preliminary version of a developing Theorem of singular manifolds and relevant examples.