Commentarii Mathematici Helvetici
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Structure in the classical knot concordance group
Tim D. Cochran (1), Kent E. Orr (2) and Peter Teichner (3)(1) Department of Mathematics, Rice University, PO Box 1892, TX 77005-1892, HOUSTON, UNITED STATES
(2) Department of Mathematics, Indiana University, IN 47405, BLOOMINGTON, UNITED STATES
(3) Department of Mathematics, University of California, CA 94720-3840, BERKELEY, UNITED STATES
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.
Keywords: Knot concordance, von Neumann signatures, Blanchfield pairing, Casson-Gordon invariants