12 problems

Let $\Lambda^s$ and $\Lambda^u$ denote the stable and unstable foliations of a pseudo-Anosov flow $\varphi$. A branching orbit is a closed orbit that lies on a leaf of $\Lambda^s$ or…

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 $M$ be a closed $3$-manifold. A pseudo-Anosov flow without negative lozenges is a pseudo-Anosov flow having no negative lozenges. Finiteness conjecture. There are finitely many…

Let $\rho$ be a strong Markovian action. A strong Markovian action is an action satisfying the strong Markovian-family conditions defined in the source. Realization conjecture for…

Let $\Phi$ be a pseudo-Anosov flow, let $\mathcal{P}$ be its bifoliated plane, and let $\mathcal{R}$ be a Markovian family for $\Phi$. A reduced Markov partition of $\Phi$ is a Mar…

Let $\Phi_1$ and $\Phi_2$ be suspension pseudo-Anosov flows. A Dehn-Goodman-Fried surgery is a surgery performed on a periodic orbit of a pseudo-Anosov flow to produce another pseu…

Let $\phi$ be the flow under consideration, let $G_+$ be its associated graph, and let $SFC(\phi,\mathcal{C})$ and $CA(\phi)$ be the chain complexes described above, where…

Let $\mathcal{F}$ be a taut foliation of an atoroidal 3-manifold $M$ which is not $\mathbb{R}$-covered. Let $\mathrm{PA}(\mathcal{F})$ be the set of pseudo-Anosov flows almost tran…

Let $\mathcal{F}$ be a taut foliation of an atoroidal 3-manifold $M$ which is not $\mathbb{R}$-covered. A foliation is almost transverse to a flow when it satisfies the almost-tran…

Let $M$ be a hyperbolic 3-manifold. A minimal P-zipper is a minimal P-zipper $Z^\pm$ for $M$, with endpoint maps denoted $e^\pm$ and corresponding spaces $P^\pm$. The converse flow…

A veering triangulation $\Delta$ on an oriented $3$-manifold $N$ determines a transitive pseudo-Anosov flow $\phi^t(\Delta,M)$ on a closed oriented $3$-manifold $M$, and a transiti…

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…