Asymptotic-Möbius maps

Georg Alexander Gruetzner (1, 2)

1 Université Paris-Saclay
2 DATASHAPE - Understanding the Shape of Data

Roughly speaking, a map between metric spaces is asymptotically Möbius if it induces quasi-Möbius maps on asymptotic cones. We show that under such maps, some large-scale notions of dimension increases: asymptotic dimension for finitely generated nilpotent groups, telescopic dimension for CAT (0) spaces.

Mots clés: Möbius geometry; large scale geometry.

Domaines: Géométrie métrique [math.MG]

Georg Alexander Gruetzner. Asymptotic-Möbius maps. 2022. ⟨hal-03746707v2⟩