Boundary actions on Bass-Serre trees yield new C*-simple groups among tubular groups, Out(BS(p,q)), and GBS_n groups, plus new purely infinite crossed products.
Tubular free by cyclic groups and the strongest Tits alternative
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abstract
We show, using Wise's equitable sets criterion, that every tubular free by cyclic group acts freely on a CAT(0) cube complex. We also show that these groups have a finite index subgroup satisfying the strongest Tits alternative, which means that every subgroup either surjects a non abelian free group or is torsion free abelian. In particular the Gersten group is the first known group virtually having this property but which is not virtually special nor virtually residually free.
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2025 1verdicts
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Boundary actions of Bass-Serre Trees and the applications to $C^*$-algebras
Boundary actions on Bass-Serre trees yield new C*-simple groups among tubular groups, Out(BS(p,q)), and GBS_n groups, plus new purely infinite crossed products.