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Commentarii Mathematici Helvetici
Article . 1993 . Peer-reviewed
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Classical knot and link concordance

Authors: Gilmer, Patrick;

Classical knot and link concordance

Abstract

In an earlier paper, the author combined the knot concordance invariants of Levine with those of Casson-Gordon by considering the homology of the 2-fold branched cyclic cover. This approach is generalized in the present paper by simultaneously considering all the \(q\)-fold branched cyclic covers for \(q\) a prime power. As an application, a new example is given of a link which is a fusion of a boundary link but which is not concordant to a boundary link. Editorial remark: It has been pointed out by Daniel Moskovich on MathOverflow, \url{https://mathoverflow.net/questions/35468/widely-accepted-mathematical-results-that-were-later-shown-to-be-wrong/36097#36097}, that the proof of Theorem 1 of this paper contains a gap, as shown by S. Friedl in his PhD-Thesis (cf. [\textit{S. Friedl}, Algebr. Geom. Topol. 4, 893--934 (2004; Zbl 1067.57003)]).

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Germany
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Keywords

Casson-Gordon invariants, 510.mathematics, slice knot, \(q\)-fold branched cyclic covers, Knots and links in the \(3\)-sphere, knot concordance invariants, concordant to a boundary link, fusion of a boundary link, Article

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
20
Average
Top 10%
Average
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gold