Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces
Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces
We show that almost nonnegatively curved m -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.