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 
@article{10_4007_annals_2010_171_343,
     author = {Vitali Kapovitch and Anton Petrunin and Wilderich Tuschmann},
     title = {Nilpotency, almost nonnegative curvature, and the gradient flow on {Alexandrov} spaces},
     journal = {Annals of mathematics},
     pages = {343--373},
     publisher = {mathdoc},
     volume = {171},
     number = {1},
     year = {2010},
     doi = {10.4007/annals.2010.171.343},
     mrnumber = {2630041},
     zbl = {1192.53040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.343/}
}
TY  - JOUR
AU  - Vitali Kapovitch
AU  - Anton Petrunin
AU  - Wilderich Tuschmann
TI  - Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces
JO  - Annals of mathematics
PY  - 2010
SP  - 343
EP  - 373
VL  - 171
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.343/
DO  - 10.4007/annals.2010.171.343
LA  - en
ID  - 10_4007_annals_2010_171_343
ER  - 
%0 Journal Article
%A Vitali Kapovitch
%A Anton Petrunin
%A Wilderich Tuschmann
%T Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces
%J Annals of mathematics
%D 2010
%P 343-373
%V 171
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.343/
%R 10.4007/annals.2010.171.343
%G en
%F 10_4007_annals_2010_171_343
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

Cité par Sources :