Characteristic random subgroups of geometric groups and free abelian\n groups of infinite rank

2014/02/15 by Lewis Bowen, Bowen, Lewis, Rostislav Grigorchuk +3 · 2 citations
Mathematics · Biochemistry, Genetics and Molecular Biology · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Amino Acid Enzymes and Metabolism

paper · pdf · doi:10.48550/arxiv.1402.3705

Abstract

We show that if G is a non-elementary word hyperbolic group, mapping class\ngroup of a hyperbolic surface or the outer automorphism group of a nonabelian\nfree group then G has 2^\ℵ₀ many continuous ergodic invariant random\nsubgroups. If G is a nonabelian free group then G has 2^\ℵ₀ many\ncontinuous G-ergodic characteristic random subgroups. We also provide a\ncomplete classification of characteristic random subgroups of free abelian\ngroups of countably infinite rank and elementary p-groups of countably\ninfinite rank.\n

Cited by

• Invariant random subgroups of groups acting on hyperbolic spaces
• Generic IRS in free groups, after Bowen

Related

• Random extensions of free groups and surface groups are hyperbolic
• Invariant random subgroups of groups acting on hyperbolic spaces
• Random subgroups, automorphisms, splittings
• Faithful invariant random subgroups in acylindrically hyperbolic groups
• Invariant random subgroups of the free group