平特五不中

Title: The failure of cost in the measure-class preserving setting.

Abstract: In measured group theory (MGT), one studies group by their actions on finite or sigma-finite measure spaces. The notion of Measure Equivalence (ME), due to Gromov, is very similar to quasi-isometry and holds many powerful invariants. We will survey treeability in the ME context, look at the main obstruction to a strengthening of ME, namely orbit equivalence (OE). We will sketch why free groups of different rank are ME, but not OE. We will then look at these notions in the measure-class preserving context and see how cost is not useful here.

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