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Structure in the classical knot concordance group

Abstract

We provide new information about the structure of the abelian group of topological concordance classes of knots in $S^3$. One consequence is that there is a subgroup of infinite rank consisting entirely of knots with vanishing Casson-Gordon invariants but whose non-triviality is detected by von Neumann signatures.

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Correspondence to Tim D. Cochran.

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Cochran, T.D., Orr, K.E. & Teichner, P. Structure in the classical knot concordance group . Comment. Math. Helv. 79, 105–123 (2004). https://doi.org/10.1007/s00014-001-0793-6

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  • DOI: https://doi.org/10.1007/s00014-001-0793-6

Mathematics Subject Classification (2000)

  • 57M25

Keywords.

  • Knot concordance
  • Von Neumann signatures
  • Blanchfield pairing
  • Casson-Gordon invariants