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arXiv · 2206.07890

Equivalent Topologies on the Contracting Boundary

Vivian He
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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 $κ$-Morse boundary with a sublinear function $κ$. The two generalizations model the Gromov boundary based on different characteristics of geodesics in Gromov hyperbolic spaces. It was suspected that the $κ$-Morse boundary contains the contracting boundary. We will prove this conjecture: when $κ=1$ is the constant function, the 1-Morse boundary and the contracting boundary are equivalent as topological spaces.

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Vivian He. 2022-06-16. Equivalent Topologies on the Contracting Boundary. https://arxiv.org/abs/2206.07890

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