4 problems

Vershik's conjecture. Despite examples in which such tensor fields have been defined and computed, there is probably no general definition of a curvature tensor for non-holonomic d…

Let $D$ be a completely nonholonomic rank $2$ distribution on an $n$-dimensional manifold, and let its class be the constant integer $m$ with $2\leq m\leq n-4$. Nonexistence conjec…

Let $M$ be a manifold, let $\omega_0$ and $\omega_1$ be symplectic structures in the same cohomology class, and suppose they can be connected by a path of symplectic structures in…

Let $\mathcal{D}$ be the diffeomorphism group of a manifold, equipped with the distribution $\mathcal T$. A path in $\mathcal{D}$ is horizontal when it is tangent to $\mathcal T$.…