3 problems

Let $M$ be a manifold, $G$ a Lie group, $X=G/H$, and let $\varphi$ be smooth. An admissible lift is a map $u$ whose gauge potential $u^{-1}du$ satisfies the admissibility condition…

Smooth representative conjecture. Every $2$-homotopy sector of finite-energy maps contains a smooth representative; equivalently,

Regularity via minors (odd $k$). If $\bigwedge^k df\in\widetilde H_{>k}$ is smooth, then $f$ is smooth.