Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities

Abstract

In this paper, we study manifolds, 𝑋Σ, with fibred singularities, more specifically, a relevant space 𝓡ᵖˢᶜ(𝑋Σ) of Riemannian metrics with positive scalar curvature. Our main goal is to prove that the space 𝓡ᵖˢᶜ(𝑋Σ) is homotopy invariant under certain surgeries on 𝑋Σ.