quasi-isometry
Sign in to saveIn 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.
~10 min read
Encyclopedic overview
13 sectionsContents
- Definition
- Examples
- Equivalence relation
- Use in geometric group theory
- Quasigeodesics and the Morse lemma
- Examples of quasi-isometry invariants of groups
- Hyperbolicity
- Growth
- Ends
- Amenability
- Asymptotic cone
- See also
- References
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.
Excerpted from Wikipedia’s “quasi-isometry” article, available under the CC BY-SA 4.0 licence.