New link invariants and applications
type: Item
instance of: scholarly article
title: New link invariants and applications
zbMATH Open document ID: 0637.57016
DOI: 10.1007/BF02564461
author: Kent E. Orr
published in: Commentarii Mathematici Helvetici
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140097
review text: This paper provides a sequence of invariants for codimension two links, which vanish on boundary links and are invariant under link cobordism. The components of a link L are not required to be spheres, but the main theorem of the paper, in which the invariants and their properties are stated, has \(H_ 1(L)=0\) as part of its hypothesis. The invariants are based on the lower central series of the link group, and as the author points out, should be compared to the classical link cobordism invariants of J. Milnor. The new invariants are related to the Sato-Levine invariant \(\beta\) (L), which is shown to vanish if either \(H_ 1(L)=0\), or if L has at least four components (and \(\beta\) (L) is defined). \textit{T. D. Cochran} has shown that almost all of these new invariants vanish when L is a spherical link, that is, when each component is a sphere [Invent. Math. 90, 635-645 (1987; Zbl 0637.57015), see the review above].
Mathematics Subject Classification ID: 57Q45
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 4038818
zbMATH Keywords: link concordance
zbMATH Keywords: codimension two links
zbMATH Keywords: boundary links
zbMATH Keywords: link cobordism
zbMATH Keywords: lower central series of the link group
zbMATH Keywords: Sato-Levine invariant
reviewed by: C. Kearton
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4038818