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Let's consider a (finitely generated) group $\Gamma$ and a coarse quotient map $q\colon\Gamma\to\mathbb{R}$. I'm interested in the 1-cocycle $\sigma\colon\Gamma\to\ell_\infty\Gamma$, defined by $\...

Let $M$ be a complete Riemannian manifold. Let us use the standard definition of "end", for example, as in this article. If $M$ has non-negative Ricci curvature, it is well-known that it has ...

I read the article of Steven Hair "A degree-theoretic proof of a coarse fixed point principle". I have the following question. I start with some main definitions from this article. A coarse ...