Filtering smooth concordance classes of topologically slice knots
type: Item
instance of: scholarly article
title: Filtering smooth concordance classes of topologically slice knots
zbMATH Open document ID: 1282.57006
author: Tim D. Cochran
author: Peter D. Horn
author: Shelly Harvey
published in: Geometry \& Topology
publication date: 2013-08-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1201.6283
review text: A knot in \(S^3\) is topologically slice if it bounds a topologically embedded 2--disk in the 4--ball, \(B^4\), and is a slice knot if it bounds a smoothly embedded 2--disk. Refining and generalizing work by \textit{T. D. Cochran} and \textit{R. E. Gompf} [Topology 27, No.4, 495--512 (1988; Zbl 0669.57003)], the article introduces a new filtration of the topological knot concordance group that induces a non--trivial filtration \({\mathcal T}_n\) of the subgroup \({\mathcal T}\) of concordance classes of topological slice knots. The gauge--theoretic and \(\tau\), \(s\), \(\epsilon\)--invariants are shown to detect knots in \({\mathcal T}/{\mathcal T}_0\) while the \(d\)--invariants detect the non--triviality of \({\mathcal T}_0/{\mathcal T}_1\).
reviewed by: James Hebda
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 6198082
zbMATH Keywords: concordance
zbMATH Keywords: slice knot
zbMATH Keywords: 4--manifold
MaRDI profile type: Publication
OpenAlex ID: W2042857121
arXiv ID: 1201.6283
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DOI: 10.2140/GT.2013.17.2103
description: scientific article; zbMATH DE number 6198082