Geodesic
Superrigidity, measure equivalence, and weak Pinsker entropy
Lewis Bowen1 ; Robin D. Tucker-Drob2
1The University of Texas at Austin, USA
2Texas A&M University, College Station, USA
Groups, geometry, and dynamics, Tome 16 (2022) no. 1, pp. 247-286

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DOI

We show that the class B, of discrete groups which satisfy the conclusion of Popa’s cocycle superrigidity theorem for Bernoulli actions, is invariant under measure equivalence. We generalize this to the setting of discrete probability measure preserving (p.m.p.) groupoids, and as a consequence we deduce that any nonamenable lattice in a product of two noncompact, locally compact second countable groups must belong to B. We also introduce a measure-conjugacy invariant called weak Pinsker entropy and show that, if G is a group in the class B, then weak Pinsker entropy is an orbit-equivalence invariant of every essentially free p.m.p. action of G.
DOI : 10.4171/ggd/647
Classification : 37-XX
Mots-clés : Entropy theory, weak Pinsker, cocycle superrigidity, Bernoulli shifts, orbit equivalence

Lewis Bowen  1   ; Robin D. Tucker-Drob  2

1 The University of Texas at Austin, USA
2 Texas A&M University, College Station, USA 
Lewis Bowen; Robin D. Tucker-Drob. Superrigidity, measure equivalence, and weak Pinsker entropy. Groups, geometry, and dynamics, Tome 16 (2022) no. 1, pp. 247-286. doi: 10.4171/ggd/647
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     title = {Superrigidity, measure equivalence, and weak {Pinsker} entropy},
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     year = {2022},
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