5 problems

Let $S$ be an infinite-type surface properly homotopy equivalent to a graph $\G$, and let $\widetilde{\Theta}:\operatorname{ExMap}(S)\to\operatorname{Map}(\G)$ be the continuous in…

Let $S$ be an infinite-type surface with compact boundary, properly homotopy equivalent to a locally finite infinite graph $\\G$, and let $\Theta$ be the induced homomorphism from…

A non-compact topological manifold without boundary is properly rigid if, whenever $N$ is another boundaryless topological manifold of the same dimension and $h\colon N\to M$ is a…

P3R–telescopic-type conjecture. The class of properly $3$-realizable groups and the class of groups of telescopic type at each end are the same.

Uncountable CSI conjecture. There exists an open, one-ended $4$-manifold $M$ such that CSI of $M$ with itself yields at least $c$ manifolds up to proper homotopy when $c$ is uncoun…