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math.GR2024
On the stability of hyperbolicity under quantitative measure equivalence
Thiebout Delabie, Juhani Koivisto, François Le Maître +1
A well-known result of Shalom says that lattices in SO are measure equivalent for all . His proof actually yields the following stronger statement: the…
math.GR2024
Balls in groups: volume, structure and growth
Romain Tessera, Matthew Tointon
We develop a fine-scale structural theory for balls of polynomial volume in finitely generated groups. Our main result shows that a polynomial-volume hypothesis on a single ball im…