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.
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The trace space of any surface group is the Poulsen simplex.
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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.
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Characters of surface groups
The trace space of any surface group is the Poulsen simplex.