II$_1$ factors and equivalence relations with distinct fundamental groups

We construct a group measure space II $_{1}$ factor that has two non-conjugate Cartan subalgebras. We show that the fundamental group of the II $_{1}$ factor is trivial, while the fundamental group of the equivalence relation associated with the second Cartan subalgebra is non-trivial. This is not absurd as the second Cartan inclusion is twisted by a 2-cocycle.

II $_{1}$ factors and equivalence relations with distinct fundamental groups

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II $_{1}$ factors and equivalence relations with distinct fundamental groups

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II11​ factors and equivalence relations with distinct fundamental groups

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II11​ factors and equivalence relations with distinct fundamental groups

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II $_{1}$ factors and equivalence relations with distinct fundamental groups

讲解博客

AI智能校验

II $_{1}$ factors and equivalence relations with distinct fundamental groups

讲解博客

AI智能校验