5 problems

Let $[\Sigma]$ be an integral homology class, with reductions $[\Sigma]^{\mathbb{R}}$ and $[\Sigma]^{\mathbb{Z}/n\mathbb{Z}}$ in the corresponding coefficient systems. The Hasse pr…

Consider the direct-limit coefficient group $\mathbb{Q}/\mathbb{Z}$ obtained from the groups $\mathbb{Z}/n\mathbb{Z}$ under the multiplication maps, equipped with the norm induced…

A variational problem may be formulated on chain spaces with coefficients in $\mathbb{R}$, $\mathbb{Z}$, and $\mathbb{Z}/n\mathbb{Z}$ for $n\geq 2$. Obstructions to the Hasse princ…

Let $k\in\mathbb{N}$, let $\mathrm{X}$ be a metric space, and let $\mathbf{M}_k(\mathrm{X})$ denote the space of metric $k$-currents on $\mathrm{X}$. Normal $k$-currents are metric…

Lang's general Flat Chain Conjecture. For every $d\in\mathbb{N}$ and $k\in\mathbb{N}\cup\{0\}$, if $T\in\mathcal{D}_k(\boldsymbol{R}^d)$ has compact support, then