Primary decomposition in the smooth concordance group of topologically slice knots

Abstract We address primary decomposition conjectures for knot concordance groups, which predict direct sum decompositions into parts. show that the smooth group of topologically slice knots has a large subgroup are true and there infinitely many parts, each infinite rank. This supports knots. also prove analogues associated graded groups bipolar filtration Among ingredients proof, we use amenable $L^2$ -signatures, Ozsváth-Szabó d -invariants Némethi’s result on Heegaard Floer homology Seifert 3-manifolds. In an appendix, present general formulation notion decomposition.