4 problems

Let $M$ be an orientable $n$-manifold equipped with a complete Riemannian metric of positive scalar curvature. For a complete Riemannian metric on $M$, say that it has at most $C$-…

Let $M$ be an open, complete, noncompact manifold without boundary whose curvature is PIC1. PIC1 open-manifold topology conjecture. $M$ is diffeomorphic to Euclidean space. This co…

Let $(M,x)$ be an open manifold with $\operatorname{Ric}\ge 0$, let $\widetilde{M}$ be its Riemannian universal cover, and let $E(M,x)$ denote the escape rate. Euclidean volume gro…

Let $M^n$ and $N^n$ be open connected smooth manifolds, each homotopy equivalent to a finite polyhedron, and let $f\colon M^n\to N^n$ be a continuous homeomorphism. Topological inv…