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

Vitali Kapovitch, Anton Petrunin, Wilderich Tuschmann

Research output: Contribution to journalArticle

15 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)343-373
Number of pages31
JournalAnnals of Mathematics
Volume171
Issue number1
DOIs
StatePublished - May 31 2010

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Alexandrov Space
Nonnegative Curvature
Nilpotency
Gradient Flow
Cover
Nilmanifolds
Homotopy Theory
Fiber Bundle
Nilpotent Group
Fundamental Group
Fiber
Curvature
Gradient
Homotopy

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Kapovitch, Vitali ; Petrunin, Anton ; Tuschmann, Wilderich. / Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces. In: Annals of Mathematics. 2010 ; Vol. 171, No. 1. pp. 343-373.
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Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces. / Kapovitch, Vitali; Petrunin, Anton; Tuschmann, Wilderich.

In: Annals of Mathematics, Vol. 171, No. 1, 31.05.2010, p. 343-373.

Research output: Contribution to journalArticle

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