Structure of the string link concordance group and Hirzebruch-type invariants

TL;DR

This paper uses Hirzebruch-type invariants from iterated p-covers to analyze the structure of the string link concordance group, revealing new homomorphisms and properties related to the Cochran-Orr-Teichner filtration.

Contribution

It introduces new invariants from p-covers that produce homomorphisms of the concordance group and its filtrations, advancing understanding of link concordance and torsion phenomena.

Findings

The invariants induce homomorphisms into L-groups over number fields.

The kernel of Harvey's ρ_n-invariant contains a subgroup with infinite rank abelianization.

Nontrivial 2-torsion examples of Bing doubles are independent over Z_2 as links.

Abstract

We employ Hirzebruch-type invariants obtained from iterated p-covers to investigate concordance of links and string links. We show that the invariants naturally give various group homomorphisms of the string link concordance group into L-groups over number fields. We also obtain homomorphisms of successive quotients of the Cochran-Orr-Teichner filtration. As an application we show that the kernel of Harvey's $\rho_n$-invariant is large enough to contain a subgroup with infinite rank abelianization, modulo local knots. As another application, we show that recently discovered nontrivial 2-torsion examples of iterated Bing doubles lying at an arbitrary depth of the Cochran-Orr-Teichner filtration are independent over $\Z_2$ as links, in an appropriate sense. We also construct similar examples of infinite order links which are independent over $\Z$.