8 problems

Solvable-filtration conjecture.

Let $\mathcal{T}$ be the group of topologically slice knots, let $\rho$ denote knot reversal, and interpret $2K=0$ in the knot concordance group. Order-two reversal conjecture. The…

Let $\mathcal{T}$ be the group of topologically slice knots, let $\mathcal{T}_\Delta$ be the subgroup appearing in the Alexander-trivial quotient, and let $\rho$ denote knot revers…

Let $\mathcal{T}$ be the group of topologically slice knots, let $\mathcal{T}_n$ be its bipolar filtration, and let … The map $\rho$ denotes knot reversal, and…

Genus-filtration quotient conjecture. $1$ For any $k\in\mathbb{N}$, $(\mathcal{C}_{TS}\cap\mathcal{G}_{k+1})/(\mathcal{C}_{TS}\cap\mathcal{G}_{k})$ contains a direct summand isomor…

Intersection conjecture. It is conjectured that

Let $\mathcal{C}_{TS}$ denote the subgroup of the smooth knot concordance group consisting of topologically slice knots. A subgroup isomorphic to $\mathbb{Z}_2^\infty$ is said to b…

Let ${\mathcal{T}}$ be the concordance subgroup of topologically slice knots, and let … be its bipolar filtration, where ${\mathcal{T}}_n$ consists of concordance classes that are…