4 problems

Let $\phi$ be a transitive pseudo-Anosov flow on an oriented closed $3$-manifold. Let $\operatorname{sing}(\phi)$ denote its singular orbits, and let positive and negative lozenges b…

Let $\mathbb{T}^n$ be a compact torus, let $\mathcal{G}$ act on it, and let $\mathcal{T}$ denote the image of $\mathbb{T}^n$ under the orbit-map parametrization…

Let $M$ be a Hausdorff manifold with a countable basis and empty boundary, and let $v$ be an arbitrary smooth vector field on $M$. Let $M/{\sim}$ denote the orbit space of $v$. Orb…

Paracompactness conjecture. If $X$ is a paracompact proper $G$-space, then the orbit space $X/G$ is paracompact.