Primary decomposition of knot concordance and von Neumann rho-invariants

Author:

Kim Min Hoon,Kim Se-Goo,Kim Taehee

Abstract

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

Funder

National Research Foundation of Korea

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference17 articles.

1. Bounds on the von Neumann dimension of 𝐿²-cohomology and the Gauss-Bonnet theorem for open manifolds;Cheeger, Jeff;J. Differential Geom.,1985

2. Amenable 𝐿²-theoretic methods and knot concordance;Cha, Jae Choon;Int. Math. Res. Not. IMRN,2014

3. [Cha19] Jae Choon Cha, Primary decomposition in the concordance group of topologically slice knots, arXiv:1910.14629, 2019.

4. 𝐿²-signatures, homology localization, and amenable groups;Cha, Jae Choon;Comm. Pure Appl. Math.,2012

5. Primary decomposition and the fractal nature of knot concordance;Cochran, Tim D.;Math. Ann.,2011

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