Kasra Rafi - The quasi-redirecting boundary

This talk was part of the Workshop on "Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics" held at the ESI July 17 — 21, 2023.

We introduce a natural notion of boundary of a proper metric space that is large and invariant under quasi-isometries. A point in this boundary is an equivalence class of quasi-geodesics that can be quasi-redirected to each other. It turns out the sublinearly-Morse boundary is a topological subspace of the quasi-redirecting boundary. We will also show that the quasi-redirecting boundary is idential to the Bowditch boundary in certain cases. This is a joint work with Yulan Qing.