5 problems

Floer's conjecture. For all such manifolds $M$, the product $m_F(A)m_F(B)$ of the operators associated with any $A,B\in H^*(M)$ should equal $m_F(C)$ for some $C\in H^*(M)$, thereb…

Arc-Floer conjecture. The numerical equality

Let $(f_t)$ be a family of functions with monodromy, and let $m$ be a positive integer. Denote by the $m$-th restricted contact locus the corresponding geometric locus associated w…

Let $L_{\wp_{\circ}}$ be the distinguished Lagrangian submanifold used to define symplectic Khovanov cohomology, and let $\beta\times\mathrm{id}$ be a braid-group action on it. The…

Product-structure conjecture. The only non-trivial products, other than products involving the unit, are