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Structure in the classical knot concordance group

Commentarii Mathematici Helvetici volume 79, pages 105–123 (2004)Cite this article

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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Authors and Affiliations

  1. Department of Mathematics, Rice University, 1892, TX 77005-1892, Houston, Texas, USA

    Tim D. Cochran

  2. Department of Mathematics, Indiana University, 47401, Bloomington, Indiana, USA

    Kent E. Orr

  3. Department of Mathematics, UC San Diego, 9500 Gilmon Drive, CA 92093-0112, La Jolla, California, USA

    Peter Teichner

Authors
  1. Tim D. Cochran
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  2. Kent E. Orr
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  3. Peter Teichner
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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