Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces

By V. Kapovitch, Anton Petrunin, Wilderich Tuschmann. 2005

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We show that almost nonnegatively curved m-dimensional manifolds are, up to finite cover, nilpotent spaces in the sense of homotopy theory and have C(m)-nilpotent fundamental groups. We also show that up to a finite cover almost nonnegatively curved manifolds are fiber bundles with simply connected fibers over nilmanifolds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a9f977793ceae50e693b7631eba3ba0373b93a52