5 problems

Let $D$ be a circular spherical divisor, meaning a topological divisor consisting of a cycle of spheres, and let $b^+(D)$ denote the positive index of its intersection form. The as…

Let $M$ be a torus bundle over $S^1$ with monodromy $A\in\operatorname{GL}_2(\mathbb{Z})$, and let $\|A\|$ denote the norm used in the source. Anisov's conjecture. The complexity o…

Let two Lagrangian torus bundles over a torus be equipped with their fibrations. A symplectomorphism is fiber-preserving when it maps fibers of one bundle to fibers of the other. M…

Torus-bundle conjecture. There exists $\varepsilon=\varepsilon(m,l,\iota)>0$ such that these assumptions imply that $M$ is a torus bundle over $X$. This is presented as an open pro…

Let $M=\mathsf{G}/\mathsf{H}$ be a homogeneous space, where $\mathsf{H}$ is a disconnected isotropy group. The identity components of $\mathsf{H}$ and $\mathsf{G}$ are denoted by…