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• W2950595413 abstract "In this paper we give a number of explicit constructions for II$_1$ factors and II$_1$ equivalence relations that have prescribed fundamental group and outer automorphism group. We construct factors and relations that have uncountable fundamental group different from $IRpos$. In fact, given any II$_1$ equivalence relation, we construct a II$_1$ factor with the same fundamental group. Given any locally compact unimodular second countable group $G$, our construction gives a II$_1$ equivalence relation $RelR$ whose outer automorphism group is $G$. The same construction does not give a II$_1$ factor with $G$ as outer automorphism group, but when $G$ is a compact group or if $G=SL^{pm}_nIR={ginGL_nIRmid det(g)=pm1}$, then we still find a type II$_1$ factor whose outer automorphism group is $G$." @default.
• W2950595413 created "2019-06-27" @default.
• W2950595413 creator A5052340674 @default.
• W2950595413 date "2010-10-18" @default.
• W2950595413 modified "2023-09-27" @default.
• W2950595413 title "Explicit examples of equivalence relations and factors with prescribed fundamental group and outer automorphism group" @default.
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