The quasi-redirecting Boundary

Yulan Qing; Kasra Rafi

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arXiv · 2406.16794

The quasi-redirecting Boundary

Yulan Qing·Kasra Rafi

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Abstract

We generalize the notion of Gromov boundary to a larger class of metric spaces beyond Gromov hyperbolic spaces. Points in this boundary are classes of quasi-geodesic rays and the space is equipped with a topology that is naturally invariant under quasi-isometries. It turns out that this boundary is compatible with other notions of boundary in many ways; it contains the sublinearly Morse boundary as a topological subspace and it matches the Bowditch boundary of relative hyperbolic spaces when the peripheral subgroups have no intrinsic hyperbolicity. We also give a complete description of the boundary of the Croke-Kleiner group where the quasi-redirecting boundary reveals a new class of QI-invariant, Morse-like quasi-geodesics.

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Yulan Qing, Kasra Rafi. 2024-06-24. The quasi-redirecting Boundary. https://arxiv.org/abs/2406.16794

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