Groups with finitely many Busemann points

Ariel Yadin; Liran Ron-George

Groups with finitely many Busemann points

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arxiv 2305.02303 v1 pith:SFJFGLR5 submitted 2023-05-03 math.GR math.MG

Liran Ron-George , Ariel Yadin This is my paper · ORCID

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keywords finitelybusemannmanyonlypointsauthorboundarycayley

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We show that an infinite finitely generated group G is virtually-Z if and only if every Cayley graph of G contains only finitely many Busemann points in its horofunction boundary. This complements a previous result of the second named author and M. Tointon.

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Groups with a finite Busemann boundary are virtually cyclic
math.GR 2025-11 conditional novelty 7.0 of 10

If a finitely generated group admits a Cayley graph with finitely many Busemann boundary points, then the group is virtually cyclic.

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