17 problems

Let $W$ be a Weinstein manifold and let $L$ be its Lagrangian skeleton. Denote by $\mathcal{W}(W)$ the wrapped Fukaya category of $W$ and by $\operatorname{MSh}(L)$ the microlocal…

Let $(W,d\theta)$ be a Weinstein manifold and let $L\subset W$ be an exact closed Lagrangian. A regular Lagrangian is an exact closed Lagrangian that is a subset of the skeleton fo…

Core--cocore Koszul duality conjecture.

Let $\mathfrak{Stein}$ and $\mathfrak{Weinstein}$ denote the spaces of Stein and Weinstein structures, respectively, and let … be the map sending a Stein structure to its associate…

Let $W$ be a flexible Weinstein structure, and let $\varphi$ be a compactly supported symplectomorphism of $W$. Bowden–Crowley conjecture. The symplectomorphism $\varphi$ is isotop…

Let $M$ be one of the Weinstein $4$-manifolds in the paper, and consider the symplectomorphisms constructed for these families. Monodromy conjecture. All of these symplectomorphism…

A flexible Weinstein structure is a Weinstein structure whose underlying Weinstein domain is flexible, and a compactly supported symplectomorphism is a symplectomorphism equal to t…

Weinstein isomorphism conjecture. For Weinstein manifolds, all of these maps should be isomorphisms.

Let $X$ be a Weinstein domain, and let $X'$ be obtained from $X$ by attaching subcritical or flexible Weinstein handles. Let $I^{\leq l}(X)$ denote the invariant defined in the pap…

Let $Y$ be a compact manifold without boundary, let $M\subset J^1Y$ be a closed tubular neighborhood of the zero-section, and let $\Lambda\subset(M,\ker(dz-pdq))$ be a Legendrian s…

Let $M$ be a Weinstein manifold of dimension $2n$, and let $L\subset M$ be a closed exact Lagrangian submanifold with vanishing Maslov class. Its homology class is…

Let $W$ be a Weinstein manifold and let $\Lambda\subset\partial W^c$ be a closed singular Legendrian. Let $W'$ be the Weinstein sector corresponding to the Weinstein pair…

Let $W$ be a Weinstein manifold and let $\Lambda\subset\partial W^c$ be a closed singular Legendrian. Let $W'$ be the Weinstein sector corresponding to the Weinstein pair…

A Weinstein domain is a compact exact symplectic manifold equipped with a Weinstein structure, and its skeleton is the union of the stable manifolds of the critical points of the a…

Let $\eta$ be a nonempty homotopy class of nondegenerate $2$-forms on a domain or manifold of dimension $2n>4$. Let $\mathfrak{Morse}_n$ be the space of Morse functions whose criti…

Let $W$ be a compact domain, and equip the spaces of Stein and Weinstein structures with the $C^\infty$ topology. A Stein structure is a pair $(J,\phi)$ consisting of an integrable…

Let $M$ be a Weinstein manifold with Liouville vector field $Y$, and let $U\subset M$ be a bounded open subset with smooth boundary such that $Y$ points outwards along $\partial U$…