7 problems

Let $\phi^t$ be a pseudo-Anosov flow on a closed oriented $3$-manifold, let $c$ be a positive/negative horizontal surgery curve, and let $n$ be a positive/negative integer, respect…

Let $\phi_1^t$ and $\phi_2^t$ be transitive Anosov flows whose stable and unstable line bundles are orientable. Fried–Ghys conjecture. The flows $\phi_1^t$ and $\phi_2^t$ are almos…

Let $(X_{\mathfrak{G}},\sigma_{\mathfrak{G}})$ be a free $\mathbb{Z}^2$-odometer, and let $\mathbf{S}:\mathbb{Z}^2\curvearrowright X$ be a minimal speedup of…

Extension conjecture. There exists a smooth equivalence $\xi: \Omega_{1} \to \Omega_{2}$ that extends $\zeta$. This would establish the possibility of extending orbit equivalences…

The analytic non-orbit-equivalence conjecture. The equivalence $E_1$ is not the least analytic equivalence relation which is not Borel reducible to an orbit equivalence.

Orbit-relation conjecture. Every $G$-orbit equivalence relation is Borel reducible to

Let $\Gamma$ be a countable group acting ergodically and essentially freely, by measure-preserving Borel automorphisms, on a standard Borel probability space $X$. Let…