11 problems

Let $M$ be a 3-manifold. Finiteness conjecture. $M$ admits only finitely many veering triangulations. This conjecture would constrain the possible veering triangulations of a fixed…

Let $\phi$ be an Anosov flow on $M$ with orientable stable and unstable foliations and no perfect fits relative to $\mathcal{C}$, and let $\Delta$ be its associated veering triangu…

Let $T^3=\boldsymbol{R}^3/\boldsymbol{Z}^3$ and suppose $n_x>0$, $n_y<0$, and $n_z>0$. Let $M_{n_x,n_y,n_z}$ be the result of the specified surgeries on the coordinate curves, with…

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…

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 $M$ be a mapping torus equipped with a veering triangulation. A minimum weight sector is a sector of minimum weight in the associated veering data, and the hypothesis of … is s…

Let $f:S\to S$ be a fully-punctured pseudo-Anosov map and consider the veering triangulation of its mapping torus. A double hook circuit is the pair of hook circuits described in t…

Let $M$ be the manifold under consideration, let $\alpha$ denote the relevant veering structure, and let $S^2(\alpha)$ be the veering sphere constructed from it. Let…

Geometric veering triangulation rarity conjecture. The probability $P_{k,\Sigma}$ decays to $0$ like $e^{-kc}$ for some constant $c=c(\Sigma)$.