Splittings of link concordance groups

We establish several results about two short exact sequences involving lower terms of the n-solvable filtration, {ℱnm} of the string link concordance group Cm. We utilize the Thom–Pontryagin construction to show that the Sato–Levine invariants μ(iijj) must vanish for 0.5-solvable links. Using this result, we show that the short exact sequence 0 →ℱ0m/ℱ 0.5m →ℱ −0.5m/ℱ 0.5m →ℱ −0.5m/ℱ 0m → 0 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 {ℱnm} in the short exact sequence 0 →ℱ−0.5m/ℱ 0m →𝒞m/ℱ 0m →𝒞m/ℱ −0.5m→0, we show that while the sequence does not split for m ≥ 3, it does indeed split for m = 2. This allows us to determine that the quotient 𝒞2/ℱ 02≅ℤ 2 ⊕ ℤ2 ⊕ ℤ2 ⊕ ℤ.