Amenable L2-Theoretic Methods and Knot Concordance

Abstract

We introduce new obstructions to topological knot concordance. These are obtained from amenable groups in Strebel's class, possibly with torsion, using a recently suggested L 2 - theoretic method due to Orr and the author. Concerning (h)-solvable knots which are defined in terms of certain Whitney towers of height h in bounding 4-manifolds, we use the obstructions to reveal new structure in the knot concordance group not detected by prior known invariants: for any n > 1 there are (n)-solvable knots which are not (n.5)-solvable (and therefore not slice) but have vanishing Cochran-Orr-Teichner L 2 -signature obstructions as well as Levine algebraic obstructions and Casson-Gordon invariants.