Timeline for Applications of the notion of of Gromov-Hausdorff distance
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 24, 2022 at 11:04 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
deleted 1 character in body
|
| Feb 28, 2011 at 14:59 | comment | added | HJRW | The definition is given in various papers of Paulin. This is probably the place to look: Paulin, Frédéric, Topologie de Gromov équivariante, structures hyperboliques et arbres réels. (French) [Equivariant Gromov topology, hyperbolic structures and real trees] Invent. Math. 94 (1988), no. 1, 53–80. | |
| Feb 28, 2011 at 9:29 | comment | added | Otis Chodosh | What is equivariant Gromov-Hausdorff convergence? | |
| Feb 27, 2011 at 15:50 | comment | added | HJRW | Mark, actually these examples employ the equivariant Gromov--Hausdorff topology. You can also use the pointed Gromov--Hausdorff topology. I agree that this isn't strictly speaking the usual Gromov--Hausdorff topology, but nonetheless I felt that they were in the spirit of the question. Asymptotic cones are one way of proving that a limit exists, but not the only way. | |
| Feb 27, 2011 at 13:31 | comment | added | user6976 | @Henry: These examples employ asymptotic cones, not GH convergence. GH limit of a sequence of metric spaces exists only if the sequence of spaces is uniformly locally compact which is true for groups of polynomial growth and not true for trees of degree at least 3. I have made the same mistake several times also before several people pointed that out to me. | |
| Feb 27, 2011 at 13:15 | history | answered | HJRW | CC BY-SA 2.5 |