Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 343-373 |
| Number of pages | 31 |
| Journal | Annals of Mathematics |
| Volume | 171 |
| Issue number | 1 |
| DOIs | |
| State | Published - May 31 2010 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
Fingerprint Dive into the research topics of 'Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces'. Together they form a unique fingerprint.
Cite this
Kapovitch, V., Petrunin, A., & Tuschmann, W. (2010). Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces. Annals of Mathematics, 171(1), 343-373. https://doi.org/10.4007/annals.2010.171.343