7 problems

Let $Y$ be a closed oriented $3$--manifold. Gompf's embedding conjecture. $Y$ admits a smooth embedding into a symplectic $4$--manifold. Such an embedding would provide a route tow…

Let … be a Seifert fibered space with $\frac{p_i}{q_i}>1$ for every $i$ and with generalized Euler invariant $\varepsilon(Y)>0$. Euler-invariant conjecture. If $Y$ smoothly embeds…

Let $Y$ be a Seifert fibered space in the setting where smooth embedding in $S^4$ requires $Y$ to be partitionable, with complementary classes defined by the partitions of the mult…

Let $f,f':N\to\mathbb R^7$ be embeddings of a closed connected orientable $4$-manifold, let $BH(f)$ and $BH(f')$ be their Boéchat–Haefliger invariants, and let $W_{f'}(f)$ be the W…

Let $N_k$ be closed connected orientable $4$-manifolds, let $f_k,f_k':N_k\to\mathbb R^7$ be embeddings, and suppose $BH(f_k)=BH(f_k')=u_k$. Let $\eta_{u_k}(f_k,f_k')$ be the relati…

Let $N$ be a closed connected orientable $4$-manifold, let $f_0,f_1:N\to S^7$ be embeddings, and let $\varphi:\partial C_{f_0}\to\partial C_{f_1}$ be an orientation-preserving bund…

Let $N$ be a closed connected orientable $4$-manifold, let $f_0,f_1:N\to S^7$ be embeddings, and let $\varphi:\partial C_{f_0}\to\partial C_{f_1}$ be an orientation-preserving Spin…