Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities - Botvinnik, Boris; Walsh, Mark G. (Symmetry, Integrability and Geometry: Methods and Applications, 2021)
In this paper, we study manifolds, Σ, with fibred singularities, more specifically, a relevant space ᵖˢᶜ(Σ) of Riemannian metrics with positive scalar curvature. Our main goal is to prove that the space ᵖˢᶜ(Σ) is homotopy invariant under certain surgeries on Σ.