In mathematics, a quasi-isometry is a function between two metric spaces that respects large-scale geometry of these spaces and ignores their small-scale details. Two metric spaces are quasi-isometric if there exists a quasi-isometry between them. The property of being quasi-isometric behaves like an equivalence relation on the class of metric spaces.
The concept of quasi-isometry is especially important in geometric group theory, following the work of Gromov.[1]
- ^ Bridson, Martin R. (2008), "Geometric and combinatorial group theory", in Gowers, Timothy; Barrow-Green, June; Leader, Imre (eds.), The Princeton Companion to Mathematics, Princeton University Press, pp. 431–448, ISBN 978-0-691-11880-2