Dynamic asymptotic dimension: relation to dynamics, topology, coarse geometry, and C-algebras Academic Article uri icon


  • 2016, Springer-Verlag Berlin Heidelberg. We introduce dynamic asymptotic dimension, a notion of dimension for actions of discrete groups on locally compact spaces, and more generally for locally compact tale groupoids. We study our notion for minimal actions of the integer group, its relation with conditions used by Bartels, Lck, and Reich in the context of controlled topology, and its connections with Gromovs theory of asymptotic dimension. We also show that dynamic asymptotic dimension gives bounds on the nuclear dimension of Winter and Zacharias for C-algebras associated to dynamical systems. Dynamic asymptotic dimension also has implications for K-theory and manifold topology: these will be drawn out in subsequent work.

published proceedings

  • Mathematische Annalen

author list (cited authors)

  • Guentner, E., Willett, R., & Yu, G.

citation count

  • 24

complete list of authors

  • Guentner, Erik||Willett, Rufus||Yu, Guoliang

publication date

  • February 2017