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A survey of classical knot concordance

Charles Livingston
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Abstract

This is survey about the classical knot concordance group, prepared for an upcoming handbook of knot theory. Topics include: the basic definitions of concordance; the theory of algebraic concordance as developed by Levine; the theory of Casson-Gordon invariants; applications of topological surgery as developed by Freedman; smooth results based on differential geometric techniques such as those of Donaldson; the filtration of the concordance group as developed by Cochran, Orr, and Teichner; and relations to classical 3-dimensional knot theory. There is also a short problem list.

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Charles Livingston. 2004-11-26. A survey of classical knot concordance. https://arxiv.org/abs/math/0307077

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