# Graphs of groups with totally disconnected Morse boundary

@inproceedings{Fioravanti2021GraphsOG, title={Graphs of groups with totally disconnected Morse boundary}, author={Elia Fioravanti and Annette Karrer}, year={2021} }

Let a finitely generated group G split as a graph of groups. If 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. When vertex groups have totally disconnected Morse boundary, this implies that ∂MG is totally disconnected. Under stronger assumptions on the edge groups (such as wideness in the sense of Druţu–Sapir), we show that Morse boundaries… Expand

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