Space of nonnegatively curved metrics and pseudoisotopies

Abstract

Let $V$ be an open manifold with complete nonnegatively curved metric such that the normal sphere bundle to a soul has no section. We prove that the souls of nearby nonnegatively curved metrics on $V$ are smoothly close. Combining this result with some topological properties of pseudoisotopies we show that for many $V$ the space of complete nonnegatively curved metrics has infinite higher homotopy groups.