L–eta–invariants and Their Approximation by Unitary Eta–invariants

Cochran, Orr and Teichner introduced L–eta–invariants to detect highly non–trivial examples of non slice knots. Using a recent theorem by Lück and Schick we show that their metabelian L–eta–invariants can be viewed as the limit of finite dimensional unitary representations. We recall a ribbon obstruction theorem proved by the author using finite dimensional unitary eta–invariants. We show that if for a knot K this ribbon obstruction vanishes then the metabelian L –eta–invariant vanishes too. The converse has been shown by the author not to be true.