6 problems

Let $n\geq 3$ be odd, and let $\Sigma_Q$ be the homotopy sphere obtained as the boundary of the manifold $Q$ in the relevant bordism group. Its class $[\Sigma_Q]$ lies in…

Let $a_0, a_1,\dots,a_n\geq 2$, and let … be the $(2n-1)$-dimensional Brieskorn link. Let $\Gamma(a_0,a_1,\dots,a_n)$ be the graph with vertices $0,1,\dots,n$, joining $i$ and $j$…

A homotopy sphere is a smooth manifold homotopy equivalent to a sphere, and a Sasakian-Einstein metric is a Sasakian metric whose associated Riemannian metric is Einstein. The prec…

Let $\sigma^8$ be the space of homotopy Hopf manifolds, let $\widetilde{\sigma}$ be the map appearing in the source, and let $\theta^7$ denote the group of homotopy seven-spheres.…

Let $\sigma^8$ be the space of homotopy Hopf manifolds, let $\mathcal L$ and $\mathrm{p}_1$ be the maps appearing in the source, and let $MO\langle 8\rangle$ be the Thom spectrum o…

Stein fillability conjecture. A homotopy sphere $\Sigma^{2q+1}$ is Stein fillable if and only if