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Structure in the classical knot concordance group

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Commentarii Mathematici Helvetici

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

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