We give a characterization of virtual surface groups as groups quasi-isometric to complete simply-connected Riemannian surfaces. Results on the equivalence up to quasi-isometry of various bounded geometry conditions for Riemannian surfaces are also obtained.
Cite this article
Sylvain Maillot, Quasi-isometries of groups, graphs and surfaces. Comment. Math. Helv. 76 (2001), no. 1, pp. 29–60DOI 10.1007/S000140050149