## Abstract

We address the primary decomposition of the knot concordance group in terms of the solvable filtration and higher order von Neumann ρ- invariants by Cochran, Orr, and Teichner. We show that for a non-negative integer n, if the connected sum of two n-solvable knots with coprime Alexander polynomials is slice, then each of the knots has vanishing von Neumann ρ- invariants of order n. This gives positive evidence for the conjecture that nonslice knots with coprime Alexander polynomials are not concordant. As an application, we show that if K is one of Cochran-Orr-Teichner's knots which are the first examples of nonslice knots with vanishing Casson-Gordon invariants, then K is not concordant to any knot with Alexander polynomial coprime to that of K.

Original language | English |
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Pages (from-to) | 439-447 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 149 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2021 |

### Bibliographical note

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