Characterizes subequivalence relations with dense orbits in the space for the ergodic hyperfinite p.m.p. equivalence relation, proves full group orbits are meager, and computes some Borel complexities using the uniform metric.
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Von Neumann algebras of Artin groups encode the number of connected components of their defining graphs except possibly for free-group-factor cases; a similar result holds for Coxeter groups absent relative hyperbolicity.
Every generalized Bratteli diagram is isomorphic to an irreducible version, with new notions of complete irreducibility linked to topological properties of the path space and tail equivalence.
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On dense orbits in the space of subequivalence relations
Characterizes subequivalence relations with dense orbits in the space for the ergodic hyperfinite p.m.p. equivalence relation, proves full group orbits are meager, and computes some Borel complexities using the uniform metric.
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On free components of Artin and Coxeter groups
Von Neumann algebras of Artin groups encode the number of connected components of their defining graphs except possibly for free-group-factor cases; a similar result holds for Coxeter groups absent relative hyperbolicity.
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Isomoprhism of generalized Bratteli diagrams
Every generalized Bratteli diagram is isomorphic to an irreducible version, with new notions of complete irreducibility linked to topological properties of the path space and tail equivalence.