On the structure of almost nonnegatively curved manifolds
type: Item
instance of: scholarly article
title: On the structure of almost nonnegatively curved manifolds
zbMATH Open document ID: 0777.53040
author: Jyh-Yang Wu
published in: Journal of Differential Geometry
publication date: 1993-02-18T00:00:00Z
review text: It follows from a well known result by Cheeger-Gromoll that a compact Riemannian manifold with nonnegative sectional curvature is, up to a finite cover, diffeomorphic to a direct product of a torus and a simply- connected manifold. In this paper a sufficient condition in terms of the diameter and the volume is given for a compact almost nonnegatively curved manifold to be, up to a finite cover, homeomorphic to the product of a torus and a simply-connected manifold. Techniques from geometric topology about controlled maps, manifold resolutions and thin \(h\)- cobordism theorem are used.
reviewed by: Hans-Bert Rademacher
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 57M12
zbMATH DE Number: 120206
zbMATH Keywords: \(h\)-cobordism theorem
zbMATH Keywords: diameter
zbMATH Keywords: volume
zbMATH Keywords: torus
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214448080
OpenAlex ID: W1548758502
Wikidata QID: Q115181264
DOI: 10.4310/JDG/1214448080
description: scientific article; zbMATH DE number 120206