6 problems

Let $X$ be a generic affine hypersurface of degree $d\geq 3$ and dimension $n\in\{3,5,6,7\}$ modulo $8$, and suppose that there is an element $\phi\in\Theta_n/bP_{n+1}$ that is not…

Let $X$ be a symplectic manifold, and let $g_0,g_1:X\rightarrow X$ be symplectomorphisms. The maps $(g_0)_*$ and $(g_1)_*$ are induced on the groups $SH_{\bullet}^M(Y,X)$ 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…

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…

Let $B^{2n}\subset\mathbb{R}^{2n}$ be the symplectic ball, let $V\subset\mathbb{R}^{2n}$ be a symplectic $2k$-dimensional subspace with $1<k<n$, and let $P_V$ be the symplectic lin…

Let $\Phi$ be the homomorphism from automorphisms of the Weyl algebra to polynomial symplectomorphisms constructed by reduction modulo an infinite prime, restriction to centers, in…