Homology boundary links and Blanchfield forms: Concordance classification and new tangle-theoretic constructions
type: Item
instance of: scholarly article
title: Homology boundary links and Blanchfield forms: Concordance classification and new tangle-theoretic constructions
zbMATH Open document ID: 0828.57016
DOI: 10.1016/0040-9383(94)90020-5
author: Tim D. Cochran
author: Kent E. Orr
published in: Topology
publication date: 1994-09-05T00:00:00Z
review text: The main motivating open problem is the classification of the set of concordance or cobordism classes of links (a link is a collection of a finite number \(m\) of nicely embedded \(n\)-spheres in the \((n + 2)\)- sphere). This classification is known for knots (the case \(m = 1)\) in dimensions \(n > 1\). Also, the classification of boundary links (i.e. admitting \(m\) disjoint Seifert surfaces) modulo boundary link cobordism is known. However, not every link is concordant to a boundary link; in fact, some years ago the present authors defined new invariants which showed that many homology boundary links are not concordant to any boundary link (it is unknown whether or not every link is concordant to a homology boundary link). The two ingredients of these invariants were a complexity associated to a ``pattern'' \(P\) and a function of the universal Blanchfield form \(B\) of the homology boundary link, which may also be viewed in terms of cobordism classes of Seifert matrices. ``The primary aim of the present paper is to show that any such pair \((P,B)\) may be realized by an explicit geometric construction. The main theorem is a corollary of a new and interesting construction for links that is useful in creating homology boundary links with prescribed properties. An important secondary goal is to classify homology boundary links modulo a suitable cobordism relation.'' For definitions and more details we recommend the extensive and carefully written introduction of the paper.
Mathematics Subject Classification ID: 57Q45
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 11E39
zbMATH DE Number: 633645
zbMATH Keywords: cobordism classes of links
zbMATH Keywords: homology boundary links
zbMATH Keywords: universal Blanchfield form
zbMATH Keywords: cobordism classes of Seifert matrices
reviewed by: Bruno Zimmermann
MaRDI profile type: Publication
full work available at URL: 0040-9383(94)90020-5
OpenAlex ID: W2083684038
description: scientific article; zbMATH DE number 633645