7 problems

Higher-dimensional torus conjecture. There exists a $T^2$-invariant contact structure $\xi$ on $T^{2n+1}$ such that

Translated-subgroup support conjecture. The support of $\pi_n(\partial B_{\epsilon}-D)$ is a union of translated subgroups of $\operatorname{Char}\pi_1(\partial B_{\epsilon}-D)$ by…

The conjecture. Under these hypotheses, the map

Let $n$, $p$, and $m$ be integers with $m\geq 2$ and $1\leq p\leq n-3$. Let $\mathcal{L}_{m\cdot p}^{n}$ denote the space of long links with $m$ components of dimension $p$ in…

Let $X$ be a simply-connected finite space. Say that $X$ has a uniform $p$-torsion bound if there is an integer $N$ such that the $p$-primary torsion in every homotopy group of $X$…

Let $M$ be a manifold with almost non-negative sectional curvature, abbreviated ANSC. The fundamental group $\pi_1(M)$ acts on the homotopy group $\pi_2(M)$ by deck transformations…

Let $X$ be a pointed space, let $n\geq 1$, and let $\widetilde{\theta}_{\iota}$ be the operation on homotopy groups induced by the distinguished class $\iota$. For $i,j\geq 1$, ide…