# Structure in the bipolar filtration of topologically slice knots

We produce a family $$\{K_p\}$$ of topologically slice knots which generates an infinite rank subgroup of the first quotient $$T_0/T_1$$ of the bipolar filtration of the concordance group.  In addition to being topologically slice, each of these knots is smoothly slice in $$D^4 \# \mathbb{CP}(2)\#\cdots\#\mathbb{CP}(2)$$ and in $$D^4 \# \overline{\mathbb{CP}(2)}\#\cdots\#\overline{\mathbb{CP}(2)}$$ (equipped with a possibly exotic smooth structure).  In addition, we show that no nontrivial linear combination of the $$K_p$$ is smoothly concordant to a knot with Alexander polynomial one.