4 problems

Let $f:{\mathbb T}^3\to\mathbb R$ be a function, and let ${\cal E}(f)$ be its exceptional set of directions, namely the directions not belonging to the stability-zone set. Novikov'…

Let $M_g^2\subset{\mathbb T}^3$ be a generic embedded surface, let $\ell$ be a soul label, and let ${\cal D}_{\ell}(M_g^2)$ denote its stability region; write $\|\ell\|$ for the no…

Let $f:\mathbb{T}^3\to\mathbb{R}$ be a smooth function and let $\mathcal{E}(f)$ be its exceptional set of directions. Let $\dim_H$ denote Hausdorff dimension. Novikov and Dynnikov'…

Let $M_g^2\subset\mathbb{T}^3$ be a generic embedded surface, let $\ell$ be a stability-zone label, and let $\mathcal{D}_{\ell}(M_g^2)$ denote its stability region. Write…