No countable family of bounded-degree graphs admitting finitely cobounded coarse quasi-actions contains every finitely generated group as a coarse embedding, resolving conjectures on the non-existence of universal Cayley graphs and quasi-isometry classes.
Groups with graphical C(6) and C(7) small cancellation presentations
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abstract
We extend fundamental results of small cancellation theory to groups whose presentations satisfy the generalizations of the classical C(6) and C(7) conditions in graphical small cancellation theory. Using these graphical small cancellation conditions, we construct lacunary hyperbolic groups and groups that coarsely contain prescribed infinite sequences of finite graphs. We prove that groups given by (possibly infinite) graphical C(7) presentations contain non-abelian free subgroups.
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math.GR 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Obstructions to coarse universality for finitely generated groups
No countable family of bounded-degree graphs admitting finitely cobounded coarse quasi-actions contains every finitely generated group as a coarse embedding, resolving conjectures on the non-existence of universal Cayley graphs and quasi-isometry classes.