Nilpotency, almost nonnegative curvature and the gradient flow

Abstract

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.

minor corrections in the proof of 2.5.1(II)

References in corpus (1)

• Ricci Curvature, Minimal Volumes, and Seiberg-Witten Theory

Cited by in corpus (11)

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• Margulis lemma and Hurewicz fibration Theorem on Alexandrov spaces
• On the geometry of some Equivariantly related manifolds
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• Locally Lipschitz contractibility of Alexandrov spaces and its applications
• Mixed curvature almost flat manifolds
• On fundamental groups of RCD spaces
• A fibration theorem for collapsing sequences of Alexandrov spaces
• Inradius collapsed manifolds
• Tori Can't Collapse to an Interval
• Margulis Lemma on $\text{RCD}(K,N)$ spaces