Polynomial splittings of metabelian von Neumann rho–invariants of knots

Kim, Se-Goo; Kim, Taehee

doi:10.1090/S0002-9939-08-09372-6

Polynomial splittings of metabelian von Neumann rho–invariants of knots
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by Se-Goo Kim and Taehee Kim

Proc. Amer. Math. Soc. 136 (2008), 4079-4087

DOI: https://doi.org/10.1090/S0002-9939-08-09372-6

Published electronically: June 4, 2008

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Abstract:

We show that if the connected sum of two knots with coprime Alexander polynomials has vanishing von Neumann $\rho$–invariants associated with certain metabelian representations, then so do both knots. As an application, we give a new example of an infinite family of knots which are linearly independent in the knot concordance group.

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