6 problems

Let $\Gamma\subset(M,\xi)$ be a contact divisor bounding a Liouville hypersurface in a contact manifold $(M,\xi)$ of dimension at least $5$. Assume that $\Gamma$ is considered in t…

Weak symplectic cobordism conjecture. The map

Naturality conjecture. The diagram of filtered Seiberg–Witten Floer cohomology groups, with horizontal maps given by the chain maps of and vertical maps given by the canonical iden…

Twisted ECH cobordism conjecture. If $c(M_+,xi_+;Omega_+)$ vanishes, then $c(M_-,xi_-;Omega_-)$ also vanishes. Moreover, if $c(M_+,xi_+;Omega_+)$ lies in the image of $U^k$ on…

Filtered sutured ECH cobordism-map conjecture. The cobordism should induce a chain map

Non-stable-homotopy conjecture. The stable Hamiltonian structures $(d\alpha_+,\alpha_+)$ and $(d\alpha_-,-\alpha_-)$ are not stably homotopic.