New constructions of slice links
type: Item
instance of: scholarly article
title: New constructions of slice links
zbMATH Open document ID: 1179.57008
DOI: 10.4171/CMH/175
author: Tim D. Cochran
author: Stefan Friedl
author: Peter Teichner
published in: Commentarii Mathematici Helvetici
publication date: 2009-06-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/0709.2148
review text: A link of \(m\) components is the image of a flat embedding \(S^1\cup\cdots\cup S^1\to S^4\) of the ordered disjoint union of \(m\) oriented copies of the circle \(S^1\) into the oriented 3-sphere \(S^3\). Two such links are called concordant if there exists a flat embedding \((S^1\cup\cdots\cup S^1)\times[0, 1]\to[0, 1]\) which restricts to the given links at the ends. A link is called (topologically) slice if it is concordant to the trivial \(m\)-component link or, equivalently, if it bounds a flat embedding of \(m\) disjoint slice disks \(D^2\cup\cdots\cup D^2\to D^4\). If the embeddings above are required to be \(C^\infty\), or smooth, then these notions are called smoothly concordant and smoothly slice. The authors use techniques of \textit{M. H. Freedman} and \textit{P. Teichner} [Invent. Math. 122, No. 3, 531--557 (1995; Zbl 0857.57018)] to prove that under certain circumstances the multi-infection of a slice link is again slice (not necessarily smoothly slice). Then they provide a general context for proving links are slice that includes many of the previously known results.
reviewed by: Alberto Cavicchioli
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 5569662
zbMATH Keywords: slice link
zbMATH Keywords: slice knot
zbMATH Keywords: concordance
zbMATH Keywords: Milnor's invariants
zbMATH Keywords: infection
zbMATH Keywords: satellite link
MaRDI profile type: Publication
arXiv ID: 0709.2148
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description: scientific article