A second order algebraic knot concordance group

Let C be the topological knot concordance group of knots S-1 subset of S-3 under connected sum modulo slice knots. Cochran, Orr and Teichner defined a filtration: C superset of F-(0) superset of F-(0.5) superset of F-(1) superset of F-(1.5) superset of F-(2) superset of ... The quotient C/F-(0.5) is isomorphic to Levine's algebraic concordance group; F-(0.5) is the algebraically slice knots. The quotient C/F-(1.5) contains all metabelian concordance obstructions. Using chain complexes with a Poincare duality structure, we define an abelian group AC(2), our second order algebraic knot concordance group. We define a group homomorphism C -> AC(2) which factors through C/F-(1.5), and we can extract the two stage Cochran-Orr-Teichner obstruction theory from our single stage obstruction group AC(2). Moreover there is a surjective homomorphism AC(2) -> C/F(0.5), and we show that the kernel of this homomorphism is nontrivial.