Infinitely-ended hyperbolic groups with homeomorphic Gromov boundaries

Alexandre Martin, Jacek Switakowski

Research output: Contribution to journalArticle

3 Citations (Scopus)
26 Downloads (Pure)

Abstract

We show that the Gromov boundary of the free product of two infinite hyperbolic groups is uniquely determined up to homeomorphism by the homeomorphism types of the boundaries of its factors. We generalize this result to graphs of hyperbolic groups over finite subgroups. Finally, we give a necessary and sufficient condition for the Gromov boundaries of any two hyperbolic groups to be homeomorphic (in terms of the topology of the boundaries of factors in terminal splittings over finite subgroups).
Original languageEnglish
Pages (from-to)273-290
Number of pages18
JournalJournal of Group Theory
Volume18
Issue number2
DOIs
Publication statusPublished - Mar 2015

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