1. Filtrations

Reversal and the bipolar filtration
Problem 1.1.
[Maggie Miller] For each $n \in \mathbb{N}$, find an $n$bipolar topologically slice knot $K$ such that $K \# K^r$ is not smoothly slice. 
4genus and the bipolar filtration
Problem 1.2.
[Jae Choon Cha] For $n \in \mathbb{N}$, are there knots in $\mathcal{T}_n$ with arbitrarily large smooth 4genus? 
Torsion and the bipolar filtration
Problem 1.3.
[Min Hoon Kim] Are all 2torsion knots 0bipolar? 
Characterization of 0bipolar knots
Problem 1.4.
[Shelly Harvey] Can one characterize 0positive, 0negative, or 0bipolar knots, either via the vanishing of invariants or geometrically?
Remark. [Arunima Ray] In the solvable filtration, a knot $K$ is 0solvable if and only if its Arf invariant vanishes.


Bipolar quotients
Problem 1.5.
Does $\mathcal{T}_n/ \mathcal{T}_{n+1}$ contain a $\mathbb{Z}^{\infty}$summand? What about a $(\mathbb{Z}/2\mathbb{Z})^{\infty}$ subgroup? 
Highly solvable knots with large 4genera.
Problem 1.6.
[Jae Choon Cha] For arbitrary $n>2$ and $g>0$ prove that there exist $n$solvable knots $K$ such that the topological 4genus of $K$ is strictly more than $g$.
Cite this as: AimPL: Smooth concordance classes of topologically slice knots, available at http://aimpl.org/concordsliceknot.