Whitney tower concordance of classical links
type: Item
instance of: scholarly article
title: Whitney tower concordance of classical links
zbMATH Open document ID: 1257.57005
author: Rob Schneiderman
author: Peter Teichner
author: James Conant
published in: Geometry \& Topology
publication date: 2012-08-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1202.3463
reviewed by: Lee P. Neuwirth
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M27
Mathematics Subject Classification ID: 57Q60
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 6068630
zbMATH Keywords: Whitney tower
zbMATH Keywords: grope
zbMATH Keywords: link concordance
zbMATH Keywords: tree
zbMATH Keywords: Arf invariant
zbMATH Keywords: Sato-Levine invariant
zbMATH Keywords: Whitney disk
zbMATH Keywords: slice link
MaRDI profile type: Publication
OpenAlex ID: W3099296048
arXiv ID: 1202.3463
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DOI: 10.2140/GT.2012.16.1419
review text: The authors continue their analyses of Whitney towers of Whitney disks. Some earlier work which this 60 page paper reiterates, elaborates, strengthens and generalizes may be found for example in: [\textit{J. Conant, R. Schneiderman} and \textit{P. Teichner}, Compos. Math. 143, No. 3, 780--810 (2007; Zbl 1128.57004), and Geom. Topol. 16, No. 1, 555--600 (2012; Zbl 1284.57007)], also \textit{R. Schneiderman} [Trans. Am. Math. Soc. 358, No. 10, 4251--4278 (2006; Zbl 1117.57021)] and \textit{R. Schneiderman} and \textit{P. Teichner} [Geometry and Topology Monographs 7, 101--134 (2004; Zbl 1090.57013)].NEWLINENEWLINEThe (framed and graded) Whitney tower here is generalized to allow twisted disks of order at least 1/2 the order of the tower. The resulting filtration of the tower is specialized to those which arise from framed links in \(S^3\). The theory developed allows determination of an obstruction to a link bounding an order \(n\) Whitney tower. Careful study of this obstruction invariant leads to the following conclusion: A link bounds an order \(n\) Whitney tower in the 4-ball if and only if the Milnor link invariants, higher order Sato-Levine invariants and higher order Arf invariants vanish up to order \(n\).NEWLINENEWLINEThe authors display and verify the commutativity of two formidable diagrams which summarize much of the paper's work.NEWLINENEWLINEA characterization of Milnor's invariants is also presented.
description: scientific article; zbMATH DE number 6068630