TY - JOUR
T1 - Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces
AU - Kapovitch, Vitali
AU - Petrunin, Anton
AU - Tuschmann, Wilderich
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2010
Y1 - 2010
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.
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U2 - 10.4007/annals.2010.171.343
DO - 10.4007/annals.2010.171.343
M3 - Article
AN - SCOPUS:77952725435
VL - 171
SP - 343
EP - 373
JO - Annals of Mathematics
JF - Annals of Mathematics
SN - 0003-486X
IS - 1
ER -