8 problems

Let $M^m$ be a connected topological manifold, and let $V_0$ be a relatively compact non-empty open subset of $M$ whose boundary is a manifold. An increasing family of relatively c…

Nonexistence conjecture. A simply connected compact manifold $X$ cannot support a minimal continuous flow, that is, there is no minimal action $\mathbb R\curvearrowright X$.

Let $\theta=(B,p,xi)$ be a family of $Rd$-bundles, and let T^% denote the covariant part of the transformation tau^% associated to the extended $A$-theory characteristic. Here…

The extended $A$-theory characteristic provides a lift associated to a family of compact topological manifolds. Connectivity conjecture. This lift becomes highly connected as the m…

Bordered-manifold Hopf brushing conjecture. Let $W$ be a compact bordered manifold (first $C^{\infty}$ and then $C^0$). Assume that $c7(W)=0$, and when $W$ is odd-dimensional that…

Topological Hopf brushing conjecture. A closed topological manifold with vanishing Euler characteristic admits a brushing.

Manifold classification conjecture. The only cases where $\mathfrak{X}_r(\mathrm{SU}(n))$ is a topological manifold are

Let $\rho\colon\Theta\to\mathbb{Z}_2$ be Rokhlin's invariant on the group $\Theta$ of homology three-spheres, defined by … where $W$ is a spin four-manifold with boundary $\Sigma$.…