4 problems

Let $B$ be a closed aspherical manifold, and let $p\colon M\to B$ and $q\colon N\to B$ be MAFs. MAF Rigidity Conjecture. The maps $p$ and $q$ are controlled homeomorphic if and onl…

Let $p\colon M\to B$ be a map whose homotopy fiber is homotopy finite. Weinberger's conjecture. The map $p$ approximately fibers modulo a Nil-obstruction. This conjecture broadens…

Let $p\colon M\to B$ be a continuous map satisfying the standing assumptions: $M$ is a connected closed topological manifold; $B$ is an aspherical closed topological manifold admit…

Let $X$ be nicely embedded in $\mathbb R^{m+n}$ for some $m\geq 3$, and suppose that $X$ has a mapping cylinder neighborhood $N=C_\phi$ of a map $\phi:\partial N\to X$, with mappin…