3 problems

Let $N$ be a fixed $n$-manifold, and let $\Phi_N:V_m\rightarrow V_{m+n}$ be the construction sending $(F\times [0,1],L)$ to $(F\times N\times [0,1],L\times N)$. Here $V_m$ denotes…

Let $n\geq 2$. A knotted $n$-sphere is an embedded $S^n$ in $D^{n+1}\times [0,1]$, and two such knots are virtually equivalent when they become equivalent after the allowed virtual…

Let $n\geq 2$. A knotted $n$-sphere is a knotted embedding of $S^n$ in $D^{n+1}\times [0,1]$, and two such knots are classically isotopic if they are related by an ambient isotopy…