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Nilpotency, almost nonnegative curvature and the gradient flow

Vitali Kapovitch·Anton Petrunin·Wilderich Tuschmann
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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.

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Vitali Kapovitch, Anton Petrunin, Wilderich Tuschmann. 2019-05-17. Nilpotency, almost nonnegative curvature and the gradient flow. https://doi.org/10.4007/annals.2010.171.343

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