A survey of classical knot concordance

2003/07/06 by Charles Livingston, Livingston, Charles · 1 citation
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/0307077

25 pages, 2 figures. Minor typographical changes

openalex publication_date 2003/07/06 · arxiv created 2004/11/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Deforming abelian elliptic SL(2,ℝ)--representations of knot groups

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