5 problems

Let $n\geq 4$. A bilipschitz bundle is a fiber bundle whose structure group lies in $\operatorname{bilipschitz}(X)$. The high-dimensional non-compactification conjecture. There exi…

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 $f:X\to Y$ be a map between simplicial complexes. A homotopy equivalence is called $Y$-triangular when its restriction $f|:f^{-1}(\tau)\to\tau$ is a homotopy equivalence for ev…

Let $X$ be a proper subset of $S^n$, let $Y$ be a metric space, and let $q:X\to Y$ be a control map. For a map $f:X\to Y$, write $qf:X\to Y$ for its composite with $q$, and let…

Let $Y$ be a finite-dimensional locally finite simplicial complex, and let a $Y$-triangular homotopy equivalence mean a homotopy equivalence whose restrictions over simplices of…