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

Vitali Kapovitch, Anton Petrunin, Wilderich Tuschmann

Research output: Contribution to journalArticle

18 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces'. Together they form a unique fingerprint.

  • Cite this