5 problems

Let $P$ be a branched standard spine embedded as a faithful flow-spine for a contact structure $cxi$ on a closed $3$-manifold $\widehat{M}$, and let $\mathcal{F}_{\xi}(P)$ denote i…

Let $(M,xi)$ be a contact $3$-manifold, and let $\tau_{(M,\xi)}$ denote its torsion, defined as the supremum of the integers $n$ for which $(M,\xi)$ contains a contact embedding of…

The sixth example consists of families of rational homology spheres of dimension $4n-1$ with $H_{2n}\approx \mathbb{Z}_3$, including links $K_{6l+2}$ and $K_{6l+4}$ related to…

Let $Y$ be an integer homology $3$-sphere bounding a Stein $4$-manifold $(X,J)$ with $c_1(J)\neq 0$. Stein representation conjecture. There exists a nontrivial homomorphism … The c…

Let $X$ be a smooth $4$-manifold with Stein structures $J_1$ and $J_2$ such that $c_1(J_1)-c_1(J_2)$ is nontorsion. Let $Y=\partial X$, and let $\xi_1$ and $\xi_2$ be the induced c…