7 problems

Let $G$ be the fundamental group of a non-positively curved graph manifold, let $X$ be its universal cover, and let $T_{\infty}$ be the Bass–Serre tree of the graph-of-groups decom…

Let $M$ be a closed aspherical $3$-manifold and let $\Gamma=\pi_1(M)$. The paper's statements numbered through concern properties of $M$ and $\Gamma$ introduced earlier in the pape…

Let $W$ be a rational homology sphere graph manifold. Circular orderability conjecture. If $\pi_1(W)$ is infinite, then $\pi_1(W)$ is circularly orderable. The conjecture isolates…

Let $N$ and $M$ be two closed graph manifolds. Let $S \looparrowright N$ and $S' \looparrowright M$ be two separable, horizontal surfaces. Quasi-isometry conjecture. There is a qua…

A CN2 manifold is a Riemannian manifold whose curvature operator has nullity of codimension at most two. Let $M$ be a compact CN2 manifold with finite volume and scalar curvature t…

Let $M^n$ be a complete CN2 manifold with finite volume, let $V$ be its set of nonflat points, and let an extension of $V$ be an open set carrying a complete flat totally geodesic…

Let $W$ be a rational homology $3$-sphere graph manifold with JSJ tori, and let $m$ be the number of these tori. For each $i$, let $[\alpha_i]$ be a rational slope associated to the…