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 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
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Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces. / Kapovitch, Vitali; Petrunin, Anton; Tuschmann, Wilderich.
In: Annals of Mathematics, Vol. 171, No. 1, 31.05.2010, p. 343-373.Research output: Contribution to journal › Article
TY - JOUR
T1 - Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces
AU - Kapovitch, Vitali
AU - Petrunin, Anton
AU - Tuschmann, Wilderich
PY - 2010/5/31
Y1 - 2010/5/31
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77952725435&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77952725435&partnerID=8YFLogxK
U2 - 10.4007/annals.2010.171.343
DO - 10.4007/annals.2010.171.343
M3 - Article
VL - 171
SP - 343
EP - 373
JO - Annals of Mathematics
JF - Annals of Mathematics
SN - 0003-486X
IS - 1
ER -