TOPOLOGICAL FULL GROUPS OF MINIMAL SUBSHIFTS AND JUST-INFINITE GROUPS
Simon Thomas · 2013
Using recent work on the algebraic structure of topological full groups of minimal subshifts, we prove that the isomorphism relation on the space of infinite finitely generated simple amenable groups is not smooth. As an application, we deduce that there does not exist an isomorphism-invariant Borel map which selects a just-infinite quotient of each infinite finitely generated group.