All Questions

Let $G$ be a f.g. group and $d$ be a word metric w.r.t. a symmetric generating set. For $g\in G$, define $|g|:=d(g,e)$, where $e$ is the group identity. For $k\in\mathbb N$, put $$n_k:=\#\{g\in G: |g|...

Recently, I came across the notion of quasi-isometries, while thinking of "discrete spaces which are surrogates for approximate continuous ones". What (metric)/geometric properties are ...