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When speaking about hyperbolic groups/spaces, one usually refers to Gromov's monograph Hyperbolic groups for their introduction. However, coarse notions of hyperbolicity can be found in some of his ...

Take two transitive graphs $X,Y$ (potentially directed and edge-labelled, e.g. Cayley graphs). Assume $X,Y$ are quasi-isometric with constant $K$, i.e. there exists a function $f:VX \to VY$ ($VX,\,VY$ ...

Let $X$ be a metric space. We say that $X$ is asymptotically geodesic if for all $\epsilon > 0$, there exists $R > 0$ such that, for all $x,y \in X$, there exists some finite sequence of points $...

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 ...