The Hausdorff- and Nagata-dimension of Möbius spaces
arXiv:1709.03254
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 Möbius spaces. This provides us with more direct methods of obtaining dimensions for boundaries of Gromov-hyperbolic spaces.
Revised version: The paper has been restructured, some proofs expanded and various typos corrected