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
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