A topological sphere theorem for arbitrary-dimensional manifolds
type: Item
instance of: scholarly article
title: A topological sphere theorem for arbitrary-dimensional manifolds
zbMATH Open document ID: 1186.53049
author: Yuliang Wen
published in: Pacific Journal of Mathematics
publication date: 2010-01-05T00:00:00Z
review text: The existing sphere theorems (like the ones proved by Coghlan and Itokawa in 1991 and the author in 2004) are related to compact, simply connected Riemannian manifolds of even dimension. If the sectional curvature, the injectivity radius and the volume of such a manifold satisfy some bound conditions, then the Riemannian manifold is homeomorphic to \(S^{n}\). In this article, the author proves a similar sphere theorem for a compact, connected Riemannian manifold, of arbitrary finite dimension, weakening the assumptions on its sectional curvature and injectivity radius.
reviewed by: Oana Constantinescu
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 5652803
zbMATH Keywords: sphere theorem
zbMATH Keywords: sectional curvature
zbMATH Keywords: injectivity radius
MaRDI profile type: Publication
full work available at URL: pjm.2010.244.193
OpenAlex ID: W2016838601
DOI: 10.2140/PJM.2010.244.193
description: scientific article; zbMATH DE number 5652803