Computation of 1-cohomology Groups and Construction of Non Orbit Equivalent Actions
نویسنده
چکیده
For each group G having an infinite normal subgroup with the relative property (T) (for instance groups of the form G = H ×K, where H is infinite with property (T) and K is arbitrary) and each countable abelian group Λ we construct free ergodic measure-preserving actions σΛ of G on the probability space such that the 1’st cohomology group of σΛ, H (σΛ, G), is equal to Char(G)×Λ. We deduce that G has uncountably many non stably orbit equivalent actions. We also calculate 1-cohomology groups and show existence of “many” non stably orbit equivalent actions for free products of groups
منابع مشابه
Calculation of 1-cohomology Groups and Construction of Non Orbit Equivalent Actions
For each group G having an infinite normal subgroup with the relative property (T) (for instance groups of the form G = H ×K, where H is infinite with property (T) and K is arbitrary) and each countable abelian group Λ we construct free ergodic measure-preserving actions σΛ on the probability space such that the 1’st cohomology group of σΛ, H (σΛ), is equal to Char(G)×Λ. We deduce that G has un...
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