4 problems

Let $M$ be the closed manifold and let $\Gamma_\infty(M)$ denote the space of smooth Riemannian metrics on $M$. Let $\mathcal{M}_{ei}$ be the set of metrics for which the set of cr…

Let $M^{n+1}$ be a closed smooth manifold, let $H_n(M;\mathbb{Z})$ denote its codimension-one homology group, and let a representative of a homology class mean a smooth hypersurfac…

Let $M^{n+1}$ be a closed smooth manifold, and let $g$ be a Baire $C^\infty$-generic Riemannian metric on $M$. A min-max $g$-minimal hypersurface is a minimal hypersurface generate…

Let $M^{n+1}$ be a closed smooth manifold. A Riemannian metric $g$ is called Baire $C^\infty$-generic if it belongs to a Baire generic subset of the space of smooth Riemannian metr…