Discrete groups with finite decomposition complexity

  • Erik W. Guentner

    University of Hawai‘i at Mānoa, Honolulu, USA
  • Romain Tessera

    Université Paris-Sud, Orsay, France
  • Guoliang Yu

    Texas A&M University, College Station, United States


In an earlier work we introduced a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. In particular, we proved the stable Borel conjecture for a closed aspherical manifold whose universal cover, or equivalently whose fundamental group, has FDC. In this note we continue our study of FDC, focusing on permanence and the relation to other coarse geometric properties. In particular, we prove that the class of FDC groups is closed under taking subgroups, extensions, free amalgamated products, HNN extensions, and direct unions. As consequences we obtain further examples of FDC groups – all elementary amenable groups and all countable subgroups of almost connected Lie groups have FDC.

Cite this article

Erik W. Guentner, Romain Tessera, Guoliang Yu, Discrete groups with finite decomposition complexity. Groups Geom. Dyn. 7 (2013), no. 2, pp. 377–402

DOI 10.4171/GGD/186