Splittings of link concordance groups

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].

CONCORDANCE OF BOUNDARY LINKS

We show that the twisted signature invariants of boundary link concordance derived from unitary representations of the free group are actually invariants of ordinary link concordance. We also show how the discontinuity locus of this signature function is determined by Seifert matrices of the link.