8 problems

Let $M$ be a $4$-dimensional manifold, let $N:T\mathcal{F}_\infty\to TM$ define a Kronecker web of $3$-web type, and let $\widetilde{N}:TM\to TM$ be an extension of $N$. The normal…

Extension conjecture. There are an open neighborhood $U\subset\Bbb C^n$ of $0$ and a Kronecker web $\cal W'$ on $U$ whose $k$-jet at $0$ agrees with $\cal W$.

Analytic approximation conjecture. There is an open subset $U'\subset U$ containing $0$ and a real-analytic Kronecker web $\cal W'$ on $U'$ whose $k$-jet at $0$ agrees with the $k$…

Local classification conjecture. There is a local isomorphism of bihamiltonian structures between $M$ near $m$ and $\Phi(\cal W)$ near $m'$.

Metaconjecture. Other integrable systems of mathematical physics should be locally isomorphic to a direct product of several copies of Example $$ .

A divergence-free Kronecker web of corank 2 is a Kronecker web of corank $2$ satisfying the divergence-free condition used in Theorem 4. Generalization conjecture. A generalization…

Let $M$ be a manifold, let $\mathcal{F}$ be the relevant foliation, and let $N:T\mathcal{F}\to TM$ be a Kronecker PNO of generic type. Extension conjecture. In any dimension, $N$ c…

Let $b\eta_1,\eta_2d$ be a Kronecker bihamiltonian structure, and let $\{\mathcal{S}'_\lambda\}$ be the Kronecker web induced on the local base of its lagrangian foliation. Gelfand…