Finiteness properties and profinite completions
Finiteness properties and profinite completions
In this note, we show that various (geometric/homological) finiteness properties are not profinite properties. For example, for all positive integers k and ℓ, there exist two finitely generated residually finite groups Γ1 and Γ2 with isomorphic profinite completions, such that Γ1 is strictly of type Fk and Γ2 of type …