6 problems

Let $N$ be a closed $n$-manifold, and let two embeddings $N\to S^{n+2}$ be given. Say that two such embeddings are almost concordant when they are related by the almost-concordance…

Consider PL embeddings of the torus $S^1\times S^1$ into $\mathbb{R}^4$, up to PL almost concordance. Three-element conjecture. The set of PL embeddings … up to PL almost concordan…

Let $N$ be a smooth manifold, and consider the Almost Embeddings Theorem (b), the cited results corresponding to [Sk02, Theorem 2.3.q], and the injectivity assertion corresponding…

Cancellation conjecture. If knots $J$ and $K\#J$ are doubly slice, then $K$ is doubly slice.

Let $n\ge 3$, and let an even $n$-stranded pretzel knot be a pretzel knot $K=P(a_1,\dots,a_n)$ with even parameters in the sense used for pretzel knots. Write $\gamma_c(K)$ for the…

Annulus-twist invariance conjecture. The 4-ball genera satisfy