Glasnik Matematicki, Vol. 58, No. 1 (2023), 75-83. \( \)

EQUIVALENT TOPOLOGIES ON THE CONTRACTING BOUNDARY

Vivian He

Department of Mathematics, University of Toronto, Canada
e-mail:vivian.he@mail.utoronto.ca

Abstract.   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.

2020 Mathematics Subject Classification.   20F65.

Key words and phrases.   Morse Boundary, Sublinearly Morse, Hyperbolic

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https://doi.org/10.3336/gm.58.1.06

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