IUMJ

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

Authors: Jae Choon Cha

Issue: Volume 58 (2009), Issue 2, 891-928

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.