Manifolds with intermediate tautness
type: Item
instance of: scholarly article
title: Manifolds with intermediate tautness
zbMATH Open document ID: 0723.53034
DOI: 10.1007/BF00181188
author: Eugene Curtin
published in: Geometriae Dedicata
publication date: 1991-01-01T00:00:00Z
review text: The main achievement of this paper is to show that there are k-taut submanifolds of Euclidean space which are not taut. \(M\subset E^ n\) is called k-taut if for every closed round ball (or complement of a ball) B the induced homomorphism \(H_ i(M\cap B)\to H_ i(M)\) is injective for \(i=0,1,...,k.\). Some examples are ellipsoids with two distinct principal radii, other examples are topologically products of type \(S^ p\times S^ q\). In particular if M is taut then \(M\times S^ 2\) is shown to admit a 0-taut embedding which is not 1-taut. There are also examples with higher codimension.
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 4192570
zbMATH Keywords: spherical two-piece-property
zbMATH Keywords: curvature surface
zbMATH Keywords: Morse inequalities
zbMATH Keywords: k- taut submanifolds
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00181188
OpenAlex ID: W1993249552
description: scientific article; zbMATH DE number 4192570