Analytic and geometric study of stratified spaces

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Diffeologies, Differential Spaces, and Symplectic Geometry (2012, background): “Unfortunately, in the literature, there are many definitions, not all of which are equivalent (see [Ś03], [Pfl01], [GM88]).”
Differential Algebraic Topology: From Stratifolds to Exotic Spheres (2010, background): “(For a nice tour through the history of stratification theory and an alternative concept of smooth stratified spaces see [Pf].”
The Yamabe problem on stratified spaces (2012, background): “Further details can be found in in the foundational monograph ofVerona [31] and the exposition by Pflaum [24].”
On static three-manifolds with positive scalar curvature (2015, methodology): “For a comprehensive exposition on singular Riemannian spaces of stratified type, see [48].”
Stably flat completions of universal enveloping algebras (2003, background): “The vector space of all A-module morphisms from X to Y is denoted by Ah(X, Y ).”
Random Fields and Geometry (2007, background): “However, there is no diffeomorphism of the plane that maps Γ to Cone({−1, 1}) – this implies that any homeomorphism ψ : Γ → Cone({−1, 1}) is not smooth as defined in [113].”
Topological complexity of smooth random functions (2011, unknown): “The basic reference for these are the monographs by Goresky and Macpherson [43] and Pflaum [67].”