Homotopy invariance of the space of metrics with positive scalar curvature on manifolds with singularities

Abstract

In this paper we study manifolds, $X_{\Sigma }$, with fibred singularities, more specifically, a relevant space ${\mathcal{R}}^{\mathrm{psc}}(X_{\Sigma })$ of Riemannian metrics with positive scalar curvature. Our main goal is to prove that the space ${\mathcal{R}}^{\mathrm{psc}}(X_{\Sigma })$ is homotopy invariant under certain surgeries on $X_{\Sigma }$.

27 pages, 4 figures

References in corpus (7)

• The Gromov-Lawson-Chernysh surgery theorem
• The positive scalar curvature cobordism category
• Metrics of positive scalar curvature and generalised Morse functions, part 1
• Positive scalar curvature on manifolds with fibered singularities
• Positive scalar curvature on simply connected spin pseudomanifolds
• Parametrized Morse Theory and Positive Scalar Curvature
• Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants

Cited by in corpus (1)

• Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants