Qing and Rafi recently introduced a new boundary for metric spaces, called the quasi-redirecting (QR) boundary. This boundary is quasi-isometry invariant, often compact, and contains the sublinearly Morse boundary as a topological subspace. While the existence of the QR boundary for all finitely generated groups remains an open question, we establish well-defined QR boundaries for several well-studied classes of groups, including relatively hyperbolic groups and all finitely generated 3-manifold groups.

We also demonstrate a connection between the QR boundary and the divergence of groups: groups with linear divergence have single-point QR boundaries, whereas certain groups with quadratic divergence, such as graph manifolds and CAT(0) admissible groups, have QR posets of height 2. Some open questions will be discussed if time permits.

This talk is based on joint work with Yulan Qing.

Zoom meeting ID: 686 4908 6485

Passcode: A group is called an ________ group if it admits an invariant mean. (8 letters, lowercase)