Jianchao Wu (Fudan University)
Finite nuclear dimension is a regularity property of C*-algebras that have played a pivotal role in the Elliott classification program of C*-algebras. It has been a key problem in the field to verify this property for crossed product C*-algebras associated to topological and C*-dynamical systems. Previous results have mainly focused on the case of free actions. In a recent preprint (joint with Hirshberg), we show that any topological action by a finitely generated virtually nilpotent group on a finite-dimensional space gives rise to a crossed product with finite nuclear dimension. This is shown by introducing a new topological-dynamical dimension concept called the long thin covering dimension. This result can be strengthened further and applied to some allosteric (and thus non-almost-finite) actions by certain wreath product groups. Another application yields the result (joint with Eckhardt) that (twisted) group C*-algebras of virtually polycyclic groups have finite nuclear dimension.
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