4 problems

Connected-sum classification conjecture. The embeddings $f\#pt$ and $f\#qt$ are isotopic if and only if

Let $X$ be a $4$-manifold with finitely presented fundamental group, and consider the main theorem of the paper, which constructs smoothly distinct surfaces that remain distinct af…

For each $g\geq 0$, let $V_0,V_1\subset S^4$ be 3-dimensional genus-$g$ handlebodies with the same boundary, $\partial V_0=\partial V_1$. A simple closed curve in $\partial V_0$ is…

Let $N$ be a closed connected orientable $n$-manifold, with $n\ge 4$. Let $N_0$ denote $N$ minus the interior of a codimension-$0$ open ball, let $H_1(N)$ denote the first homology…