The bipolar filtration of topologically slice knots

The bipolar filtration of Cochran, Harvey and Horn presents a framework of the study of
deeper structures in the smooth concordance group of topologically slice knots. We show
that the graded quotient of the bipolar filtration of topologically slice knots has infinite rank
at each stage greater than one. To detect nontrivial elements in the quotient, the proof
simultaneously uses higher order amenable Cheeger-Gromov L^2 rho-invariants and infinitely
many Heegaard Floer correction term d-invariants. This is joint work with Jae Choon Cha.