5 problems

Let $(X,d)$ be a proper metric space and let $n\in\mathbb{N}_0$. Let $H\mathcal{X}_*(X)$ denote coarse homology. Coarse Hurewicz conjecture. There is a natural morphism … that make…

Coarse mapping-space conjecture. The coarse homotopy group $\pi_n^c(X,\omega)$ is isomorphic to the group, or pointed set when appropriate, of base-ray-preserving coarse homotopy c…

Let $X$ be a ladder consisting of two rays joined at height $0$ and rungs of lengths $l_m\in\mathbb{N}$ at heights $h_m\in\mathbb{N}$, where $(h_m)$ is strictly increasing, and equ…

Let $X$ and $Y$ be compact metric spaces with finite shape dimension, let $\mathfrak{a}:cX\to cY$ be a coarse map, and suppose that $M_X$ has $t\in\mathbb{N}$ ends. Choose…

Let $\mathbb{H}=\bigvee_{j\in\mathbb{N}}S^1_j$ be the Hawaiian earring with wedge point $x_0$, and let $c\mathbb{H}$ be its cone. Write $F_h=\pi_1(\bigvee_{j=1}^hS^1_j,x_0)$ for th…