Nilpotency, almost nonnegative curvature and the gradient flow

Vitali Kapovitch; Anton Petrunin; Wilderich Tuschmann

doi:10.4007/annals.2010.171.343

Nilpotency, almost nonnegative curvature and the gradient flow

Differential Geometry 2019-05-21 v6

Authors: 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.

Keywords

nilpotent groups almost contact manifolds algebraic topology

Cite

@article{arxiv.math/0506273,
  title  = {Nilpotency, almost nonnegative curvature and the gradient flow},
  author = {Vitali Kapovitch and Anton Petrunin and Wilderich Tuschmann},
  journal= {arXiv preprint arXiv:math/0506273},
  year   = {2019}
}