Structure of the String Link Concordance Group and Hirzebruch-type Invariants

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. We illustrate that our invariant reveals much information that Harvey's rho(n)-invariant does not extract, by showing that the kernel of the rho(n)-invariant is large enough to contain a subgroup with infinite rank abelianization modulo local knots. As another application, we show that concordance classes of recently discovered non-slice iterated Bing doubles are independent in an appropriate sense.