On the space of riemannian metrics satisfying surgery stable curvature conditions

We utilize a condition for algebraic curvature operators called surgery stability as suggested by the work of Hoelzel to investigate space riemannian metrics over closed manifolds satisfying these conditions. Our main result is parametrized Gromov–Lawson construction with not necessarily trivial normal bundles and shows that homotopy type this invariant under surgeries suitable codimension. This generalization well-known theorem Chernysh Walsh positive scalar curvature. As an application our method, we show on quaternionic projective spaces are equivalent spheres.