Almost-invariant Lipschitz functions on free groups are within delta/2 of an invariant homomorphism, and finitely presented groups admit group-dependent linear approximation.
Calegari.scl, volume 20 ofMSJ Memoirs
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Almost-invariant elements of group actions on Lip$_0$ spaces
Almost-invariant Lipschitz functions on free groups are within delta/2 of an invariant homomorphism, and finitely presented groups admit group-dependent linear approximation.