Publication date: 30 June 2023
Volume: Vol 58
Issue: Svezak 1
Pages: 75-83
DOI: 10.3336/gm.58.1.06
Izvorni znanstveni članak
https://doi.org/10.3336/gm.58.1.06
Equivalent topologies on the contracting boundary
Vivian He
orcid.org/0000-0002-4089-9562
; Department of Mathematics, University of Toronto, Canada
The contracting boundary of a proper geodesic metric space generalizes the Gromov boundary of a hyperbolic space. It consists of contracting geodesics up to bounded Hausdorff distances. Another generalization of the Gromov boundary is the \(\kappa\)–Morse boundary with a sublinear function \(\kappa\). The two generalizations model the Gromov boundary based on different characteristics of geodesics in Gromov hyperbolic spaces. It was suspected that the \(\kappa\)–Morse boundary contains the contracting boundary. We will prove this conjecture: when \(\kappa =1\) is the constant function, the 1-Morse boundary and the contracting boundary are equivalent as topological spaces.
Morse Boundary, Sublinearly Morse, Hyperbolic
304392
20.6.2023.
Posjeta: 200 *