27 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 $M$ be a fixed closed $3$-manifold. A pseudo-Anosov flow is a flow with the usual pseudo-Anosov dynamical structure, and two such flows are equivalent when they are related by…

Let $M$ be a closed hyperbolic $3$-manifold, and let $Z^\pm$ be a minimal zipper for $M$. For a quasigeodesic pseudo-Anosov flow on $M$, let $P$ be the flowspace, let $P^\pm$ be th…

Landry–Minsky–Taylor's conjecture. As actions on circles, all universal circles for non-$\mathbb{R}$-covered foliations arise as flowspace boundaries of transverse almost pseudo-An…

A positive/negative horizontal surgery curve for a pseudo-Anosov flow is a steady curve of the corresponding sign, and horizontal Goodman surgery is defined by cutting along a tran…

A transitive pseudo-Anosov flow is a pseudo-Anosov flow on a closed $3$-manifold whose flow has a dense orbit, and two such flows are orbit equivalent when there is a homeomorphism…

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 $Y$ be a closed $3$-manifold, and consider pseudo-Anosov flows on $Y$, where two flows are regarded as equivalent when they are equivalent in the sense intended by the source.…

Let a group $G$ admit an Anosov-like action on a bifoliated plane. Mann's Anosov-like action conjecture. Then $G$ is the fundamental group of a $3$-manifold with a pseudo-Anosov fl…

Let $M$ be an atoroidal $3$-manifold and let $\mathcal{F}$ be a taut foliation on $M$. Transverse pseudo-Anosov flow conjecture. The foliation $\mathcal{F}$ admits an almost-transv…

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…

Finiteness conjecture. On any given closed, oriented $3$-manifold, there are a finite number of transitive pseudo-Anosov flows up to orbit equivalence.

Let $M$ be a closed oriented $3$-manifold, let $\mathcal{C}$ be a finite collection of curves in $M$ consisting of orbits of a pseudo-Anosov flow $\phi^t$, and let $\Delta$ be a ve…

A horizontal surgery operation on veering triangulations modifies a veering triangulation along a horizontal surgery curve, while horizontal Goodman surgery performs the correspond…

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…

Let $B$ be a veering branched surface and let $\alpha$ be a vertical surgery curve. Assume the correspondence in the source's theorem relating veering branched surfaces to pseudo-A…

Let $B$ be a veering branched surface, let $\alpha$ be a vertical surgery curve, and let the associated pseudo-Anosov flow have a periodic orbit corresponding to $\alpha$. Vertical…