The Hausdorff- and Nagata-dimension of M\"obius spaces
Merlin Incerti-Medici
TL;DR
This paper investigates the dimensions of M"obius spaces through cross ratios, establishing invariance of Hausdorff- and Nagata-dimension, and offers new methods for determining boundary dimensions of Gromov-hyperbolic spaces.
Contribution
It introduces and proves the invariance of Hausdorff- and Nagata-dimension in M"obius spaces, providing direct techniques for boundary dimension analysis.
Findings
Hausdorff- and Nagata-dimension are invariants of M"obius spaces
New methods for calculating boundary dimensions of Gromov-hyperbolic spaces
Cross ratios serve as a foundational tool for dimension notions
Abstract
We study cross ratios from an axiomatic viewpoint and show that a space equipped with a cross ratios carries several notions of dimension. Specifically, we introduce notions of Hausdorff- and Nagata-dimension and prove that they are invariants of M\"obius spaces. This provides us with more direct methods of obtaining dimensions for boundaries of Gromov-hyperbolic spaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Analytic and geometric function theory