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.
Citation
Igor Belegradek. F. Thomas Farrell. Vitali Kapovitch. "Space of nonnegatively curved metrics and pseudoisotopies." J. Differential Geom. 105 (3) 345 - 374, March 2017. https://doi.org/10.4310/jdg/1488503001
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