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

Vitali Kapovitch; Anton Petrunin; Wilderich Tuschmann

doi:10.4007/annals.2010.171.343

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

Vitali Kapovitch
, Anton Petrunin
, Wilderich Tuschmann

Research output: Contribution to journal › Article › peer-review

38 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 language	English (US)
Pages (from-to)	343-373
Number of pages	31
Journal	Annals of Mathematics
Volume	171
Issue number	1
DOIs	https://doi.org/10.4007/annals.2010.171.343
State	Published - 2010

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.4007/annals.2010.171.343

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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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AU - Kapovitch, Vitali

AU - Petrunin, Anton

AU - Tuschmann, Wilderich

PY - 2010

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N2 - 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.

AB - 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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UR - https://www.scopus.com/pages/publications/77952725435#tab=citedBy

U2 - 10.4007/annals.2010.171.343

DO - 10.4007/annals.2010.171.343

M3 - Article

AN - SCOPUS:77952725435

SN - 0003-486X

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EP - 373

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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