Cocycle superrigidity for profinite actions of irreducible lattices
Daniel Drimbe
KU Leuven, BelgiumAdrian Ioana
Unuversity of California San Diego, La Jolla, USAJesse Peterson
Vanderbilt University, Nashville, USA
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Abstract
Let be an irreducible lattice in a product of two locally compact groups and assume that is densely embedded in a profinite group . We give necessary conditions which imply that the left translation action is “virtually” cocycle superrigid: any cocycle with values in a countable group is cohomologous to a cocycle which factors through the map for some finite quotient group of . As a corollary, we deduce that any ergodic profinite action of is virtually cocycle superrigid and virtually W-superrigid for any finite nonempty set of primes .
Cite this article
Daniel Drimbe, Adrian Ioana, Jesse Peterson, Cocycle superrigidity for profinite actions of irreducible lattices. Groups Geom. Dyn. 17 (2023), no. 1, pp. 315–329
DOI 10.4171/GGD/700