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math.GR2026
Exactness and the topology of the space of invariant random equivalence relations
Héctor Jardón-Sánchez, Sam Mellick, Antoine Poulin +1
We characterize exactness of a countable group in terms of invariant random equivalence relations (IREs) on . Specifically, we show that is exact if and only if every…
math.GR2025
Unimodular random graphs with Property (T) have cost one
Åukasz Grabowski, Héctor Jardón-Sánchez, Sam Mellick
Hutchcroft and Pete showed that countably infinite groups with Property (T) admit cost one actions, resolving a question of Gaboriau. We give a streamlined proof of their theorem,…