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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Authors: Botvinnik, Boris, Walsh, Mark G.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211315
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities. Boris Botvinnik and Mark G. Walsh. SIGMA 17 (2021), 034, 27 pages

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.