We prove that many spaces of positive scalar curvature (psc) metrics have the homotopy type infinite loop spaces. Our result in particular applies to path component round metric inside R+(Sd) if d≥6. To achieve goal, we study cobordism category manifolds with curvature. Under suitable connectivity conditions, can identify fiber forgetful map from psc ordinary a delooping metrics. This uses vers...

We completely characterize the sectional curvature of all 13-dimensional Bazaikin spaces. In particular, we show that spaces admit a quasi-positively curved Riemannian metric, and that, up to isometry, there is unique space which almost positively but not curved.