Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces


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.


Vitali Kapovitch

Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada

Anton Petrunin

Department of Mathematics, Pennsylvania State University, University Park, State College, PA 16802, United States

Wilderich Tuschmann

Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn–Straße 4-8, D-24118 Kiel, Germany