Splittings of link concordance groups

Abstract

We establish several results about two short exact sequences involving lower terms of the [Formula: see text]-solvable filtration, [Formula: see text] of the string link concordance group [Formula: see text]. We utilize the Thom–Pontryagin construction to show that the Sato–Levine invariants [Formula: see text] must vanish for 0.5-solvable links. Using this result, we show that the short exact sequence [Formula: see text] does not split for links of two or more components, in contrast to the fact that it splits for knots. Considering lower terms of the filtration [Formula: see text] in the short exact sequence [Formula: see text], we show that while the sequence does not split for [Formula: see text], it does indeed split for [Formula: see text]. This allows us to determine that the quotient [Formula: see text].