Commentarii Mathematici Helvetici


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Volume 76, Issue 1, 2001, pp. 29–60
DOI: 10.1007/s000140050149

Quasi-isometries of groups, graphs and surfaces

Sylvain Maillot[1]

(1) Institut de Mathématiques et de Modélisation, Université Montpellier II, Case Courrier 051, Place Eugène Bataillon, 34095, MONTPELLIER CEDEX, FRANCE

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.

Keywords: Quasi-isometry, surface group, free group, isoperimetric inequality.

Maillot Sylvain: Quasi-isometries of groups, graphs and surfaces. Comment. Math. Helv. 76 (2001), 29-60. doi: 10.1007/s000140050149