Null k-cobordant links in \(S^ 3\)
type: Item
instance of: scholarly article
title: Null k-cobordant links in \(S^ 3\)
zbMATH Open document ID: 0734.57009
DOI: 10.1007/BF02566653
published in: Commentarii Mathematici Helvetici
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140237
review text: A k-cobordism between links with m components in \(S^ 3\) is given by m compact connected oriented surfaces \(V_ i\), disjointly embedded in \(S^ 3\times I\), with prescribed boundary behaviour and such that certain elements of \(\pi_ 1(V_ i)\), when pushed into the complement, lie already in the k-th term of the lower central series of the fundamental group of \(S^ 3\times I-\cup V_ i\). In the present paper the resulting equivalence relation is compared to link homotopy. In particular, it is shown that if a link is null k-cobordant then all its \({\bar \mu}\)-invariants with length less than or equal to 2k vanish. This completes the proof of a conjecture of Cochran and Orr.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 4214955
zbMATH Keywords: cobordism
zbMATH Keywords: links
zbMATH Keywords: link homotopy
zbMATH Keywords: \({\bar \mu }\)-invariants
author: Xiao-Song Lin
reviewed by: Ulrich Koschorke
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4214955