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

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.

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Authors

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