Let be the topological knot concordance group of knots under connected sum modulo slice knots. Cochran, Orr and Teichner defined a filtration:
The quotient is isomorphic to Levine’s algebraic concordance group; is the algebraically slice knots. The quotient contains all metabelian concordance obstructions.
Using chain complexes with a Poincaré duality structure, we define an abelian group , our second order algebraic knot concordance group. We define a group homomorphism which factors through , and we can extract the two stage Cochran–Orr–Teichner obstruction theory from our single stage obstruction group . Moreover there is a surjective homomorphism , and we show that the kernel of this homomorphism is nontrivial.
"A second order algebraic knot concordance group." Algebr. Geom. Topol. 12 (2) 685 - 751, 2012. https://doi.org/10.2140/agt.2012.12.685