On a Class of Type Ii1 Factors with Betti Numbers Invariants
نویسنده
چکیده
We prove that a type II1 factor M can have at most one Cartan subalgebra A satisfying a combination of rigidity and compact approximation properties. We use this result to show that within the class HT of factors M having such Cartan subalgebras A ⊂ M , the Betti numbers of the standard equivalence relation associated with A ⊂ M ([G2]), are in fact isomorphism invariants for the factorsM , β HT n (M), n ≥ 0. The classHT is closed under amplifications and tensor products, with the Betti numbers satisfying β HT
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