Geodesic
Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces
Vitali Kapovitch1 ; Anton Petrunin2 ; Wilderich Tuschmann3
1 Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
2 Department of Mathematics, Pennsylvania State University, University Park, State College, PA 16802, United States
3 Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn–Straße 4-8, D-24118 Kiel, Germany
Annals of mathematics, Tome 171 (2010) no. 1, pp. 343-373.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2010.171.343

Vitali Kapovitch 1 ; Anton Petrunin 2 ; Wilderich Tuschmann 3

1 Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
2 Department of Mathematics, Pennsylvania State University, University Park, State College, PA 16802, United States
3 Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn–Straße 4-8, D-24118 Kiel, Germany 
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Vitali Kapovitch; Anton Petrunin; Wilderich Tuschmann. Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces. Annals of mathematics, Tome 171 (2010) no. 1, pp. 343-373. doi : 10.4007/annals.2010.171.343. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.343/

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