Vol. 317, No. 2, 2022

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Connected components of Morse boundaries of graphs of groups

Elia Fioravanti and Annette Karrer

Vol. 317 (2022), No. 2, 339–361
Abstract

Let a finitely generated group G split as a graph of groups. If the edge groups are undistorted and do not contribute to the Morse boundary MG, we show that every connected component of MG with at least two points originates from the Morse boundary of a vertex group.

Under stronger assumptions on the edge groups (such as wideness in the sense of Druţu–Sapir), we show that the Morse boundaries of the vertex groups are topologically embedded in MG.

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Keywords
Morse boundary, graph of groups, totally disconnected, relatively wide
Mathematical Subject Classification
Primary: 20E08, 20F65, 20F67
Milestones
Received: 1 November 2021
Revised: 20 January 2022
Accepted: 22 January 2022
Published: 14 July 2022
Authors
Elia Fioravanti
Max Planck Institute for Mathematics
Bonn
Germany
Annette Karrer
Technion
Israel Institute of Technology
Haifa
Israel